On Classification of Modular Tensor Categories View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2009-12

AUTHORS

Eric Rowell, Richard Stong, Zhenghan Wang

ABSTRACT

We classify all unitary modular tensor categories (UMTCs) of rank ≤ 4. There are a total of 35 UMTCs of rank ≤ 4 up to ribbon tensor equivalence. Since the distinction between the modular S-matrix S and −S has both topological and physical significance, so in our convention there are a total of 70 UMTCs of rank ≤ 4. In particular, there are two trivial UMTCs with S = (±1). Each such UMTC can be obtained from 10 non-trivial prime UMTCs by direct product, and some symmetry operations. Explicit data of the 10 non-trivial prime UMTCs are given in Sect. 5. Relevance of UMTCs to topological quantum computation and various conjectures are given in Sect. 6. More... »

PAGES

343-389

References to SciGraph publications

  • 1989-06. Classical and quantum conformal field theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2002-06. Simulation of Topological Field Theories¶by Quantum Computers in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2005-09. Modular Data: The Algebraic Combinatorics of Conformal Field Theory in JOURNAL OF ALGEBRAIC COMBINATORICS
  • 2002-06. The Two-Eigenvalue Problem and Density¶of Jones Representation of Braid Groups in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2002-06. A Modular Functor Which is Universal¶for Quantum Computation in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1993-10. Chern-Simons theory with finite gauge group in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1991-08. Markov traces and II1 factors in conformal field theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1990-04. Topological gauge theories and group cohomology in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2000-02. Catégories prémodulaires, modularisations et invariants des variétés de dimension 3 in MATHEMATISCHE ANNALEN
  • 2005-12. Density of the SO(3) TQFT Representation of Mapping Class Groups in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1993. Quantum Groups, Quantum Categories and Quantum Field Theory in NONE
  • 2009-05. Integral modular data and congruences in JOURNAL OF ALGEBRAIC COMBINATORICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00220-009-0908-z

    DOI

    http://dx.doi.org/10.1007/s00220-009-0908-z

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1006159661


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Texas A&M University", 
              "id": "https://www.grid.ac/institutes/grid.264756.4", 
              "name": [
                "Department of Mathematics, Texas A&M University, 77843, College Station, TX, U.S.A."
              ], 
              "type": "Organization"
            }, 
            "familyName": "Rowell", 
            "givenName": "Eric", 
            "id": "sg:person.013246237501.57", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013246237501.57"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "name": [
                "Center for Communications Research, 4320 Westerra Court, 92121-1969, San Diego, CA, U.S.A."
              ], 
              "type": "Organization"
            }, 
            "familyName": "Stong", 
            "givenName": "Richard", 
            "id": "sg:person.01234166050.20", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01234166050.20"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of California, Santa Barbara", 
              "id": "https://www.grid.ac/institutes/grid.133342.4", 
              "name": [
                "Microsoft Station Q, University of California, CNSI Bldg, Rm 2237, 93106-6105, Santa Barbara, CA, U.S.A."
              ], 
              "type": "Organization"
            }, 
            "familyName": "Wang", 
            "givenName": "Zhenghan", 
            "id": "sg:person.014043620101.93", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014043620101.93"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/0370-2693(90)91593-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003832335"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(90)91593-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003832335"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1098/rsta.1989.0082", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004613370"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002200200645", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006311725", 
              "https://doi.org/10.1007/s002200200645"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(98)00111-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009031292"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.75.032322", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009445047"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.75.032322", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009445047"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-005-1382-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011308383", 
              "https://doi.org/10.1007/s00220-005-1382-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-005-1382-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011308383", 
              "https://doi.org/10.1007/s00220-005-1382-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10801-005-2514-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012459886", 
              "https://doi.org/10.1007/s10801-005-2514-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10801-005-2514-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012459886", 
              "https://doi.org/10.1007/s10801-005-2514-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10801-005-2514-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012459886", 
              "https://doi.org/10.1007/s10801-005-2514-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.532333", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015354582"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0003-4916(02)00018-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015449553"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0003-4916(02)00018-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015449553"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.98.160409", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019178285"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.98.160409", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019178285"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(95)00172-h", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019591000"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.aop.2005.10.005", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025107810"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(94)91226-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025921751"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(94)91226-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025921751"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/revmodphys.80.1083", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028121061"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/revmodphys.80.1083", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028121061"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0040-9383(92)90015-a", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028642877"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1029526220", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0084244", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029526220", 
              "https://doi.org/10.1007/bfb0084244"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0084244", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029526220", 
              "https://doi.org/10.1007/bfb0084244"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10801-008-0139-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031435106", 
              "https://doi.org/10.1007/s10801-008-0139-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10801-008-0139-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031435106", 
              "https://doi.org/10.1007/s10801-008-0139-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002200200636", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031600564", 
              "https://doi.org/10.1007/s002200200636"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02096988", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033632840", 
              "https://doi.org/10.1007/bf02096988"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02096988", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033632840", 
              "https://doi.org/10.1007/bf02096988"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/00018739500101566", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034510423"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/00018739500101566", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034510423"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01238857", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034666835", 
              "https://doi.org/10.1007/bf01238857"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/crll.2005.2005.581.31", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040019718"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002200200635", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043125022", 
              "https://doi.org/10.1007/s002200200635"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0273-0979-02-00964-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044082506"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002080050011", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044599308", 
              "https://doi.org/10.1007/s002080050011"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevb.77.235108", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044867752"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevb.77.235108", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044867752"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevb.71.045110", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047264319"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevb.71.045110", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047264319"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1112/s0024611503014187", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049189079"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02096860", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049272767", 
              "https://doi.org/10.1007/bf02096860"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02096860", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049272767", 
              "https://doi.org/10.1007/bf02096860"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0894-0347-98-00253-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049305288"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0022-4049(02)00248-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049588929"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0022-4049(02)00248-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049588929"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0370-2693(96)01662-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051813315"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02352496", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051824934", 
              "https://doi.org/10.1007/bf02352496"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02352496", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051824934", 
              "https://doi.org/10.1007/bf02352496"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(91)90407-o", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052458791"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(91)90407-o", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052458791"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1073/pnas.95.1.98", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052652635"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevb.78.155109", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053383637"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevb.78.155109", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053383637"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0219199708003162", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062991261"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4007/annals.2005.162.581", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071866940"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/mrl.2003.v10.n2.a5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072462218"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/conm/413/07848", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1089201948"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/9789812772527_0005", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1096058469"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/9781400882533", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1096910407"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1098924973", 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/advsov/016.2/03", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1101567767"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.17323/1609-4514-2008-8-1-111-118", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1111409547"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2009-12", 
        "datePublishedReg": "2009-12-01", 
        "description": "We classify all unitary modular tensor categories (UMTCs) of rank \u2264 4. There are a total of 35 UMTCs of rank \u2264 4 up to ribbon tensor equivalence. Since the distinction between the modular S-matrix S and \u2212S has both topological and physical significance, so in our convention there are a total of 70 UMTCs of rank \u2264 4. In particular, there are two trivial UMTCs with S = (\u00b11). Each such UMTC can be obtained from 10 non-trivial prime UMTCs by direct product, and some symmetry operations. Explicit data of the 10 non-trivial prime UMTCs are given in Sect. 5. Relevance of UMTCs to topological quantum computation and various conjectures are given in Sect. 6.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s00220-009-0908-z", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136216", 
            "issn": [
              "0010-3616", 
              "1432-0916"
            ], 
            "name": "Communications in Mathematical Physics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "292"
          }
        ], 
        "name": "On Classification of Modular Tensor Categories", 
        "pagination": "343-389", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "1d577c6cc450d0c8635e176ac74f674b710c7d75f910cb6f8194f545710959af"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00220-009-0908-z"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1006159661"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00220-009-0908-z", 
          "https://app.dimensions.ai/details/publication/pub.1006159661"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T14:29", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000373_0000000373/records_13087_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2Fs00220-009-0908-z"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00220-009-0908-z'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00220-009-0908-z'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00220-009-0908-z'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00220-009-0908-z'


     

    This table displays all metadata directly associated to this object as RDF triples.

    228 TRIPLES      21 PREDICATES      73 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00220-009-0908-z schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Ndb89c408336a4d34b8f2a5acd584f7a9
    4 schema:citation sg:pub.10.1007/bf01238857
    5 sg:pub.10.1007/bf02096860
    6 sg:pub.10.1007/bf02096988
    7 sg:pub.10.1007/bf02352496
    8 sg:pub.10.1007/bfb0084244
    9 sg:pub.10.1007/s002080050011
    10 sg:pub.10.1007/s00220-005-1382-x
    11 sg:pub.10.1007/s002200200635
    12 sg:pub.10.1007/s002200200636
    13 sg:pub.10.1007/s002200200645
    14 sg:pub.10.1007/s10801-005-2514-2
    15 sg:pub.10.1007/s10801-008-0139-y
    16 https://app.dimensions.ai/details/publication/pub.1029526220
    17 https://app.dimensions.ai/details/publication/pub.1098924973
    18 https://doi.org/10.1016/0040-9383(92)90015-a
    19 https://doi.org/10.1016/0370-2693(90)91593-z
    20 https://doi.org/10.1016/0370-2693(94)91226-2
    21 https://doi.org/10.1016/0370-2693(95)00172-h
    22 https://doi.org/10.1016/0550-3213(91)90407-o
    23 https://doi.org/10.1016/j.aop.2005.10.005
    24 https://doi.org/10.1016/s0003-4916(02)00018-0
    25 https://doi.org/10.1016/s0022-4049(02)00248-7
    26 https://doi.org/10.1016/s0370-2693(96)01662-0
    27 https://doi.org/10.1016/s0550-3213(98)00111-4
    28 https://doi.org/10.1063/1.532333
    29 https://doi.org/10.1073/pnas.95.1.98
    30 https://doi.org/10.1080/00018739500101566
    31 https://doi.org/10.1090/advsov/016.2/03
    32 https://doi.org/10.1090/conm/413/07848
    33 https://doi.org/10.1090/s0273-0979-02-00964-3
    34 https://doi.org/10.1090/s0894-0347-98-00253-7
    35 https://doi.org/10.1098/rsta.1989.0082
    36 https://doi.org/10.1103/physreva.75.032322
    37 https://doi.org/10.1103/physrevb.71.045110
    38 https://doi.org/10.1103/physrevb.77.235108
    39 https://doi.org/10.1103/physrevb.78.155109
    40 https://doi.org/10.1103/physrevlett.98.160409
    41 https://doi.org/10.1103/revmodphys.80.1083
    42 https://doi.org/10.1112/s0024611503014187
    43 https://doi.org/10.1142/9789812772527_0005
    44 https://doi.org/10.1142/s0219199708003162
    45 https://doi.org/10.1515/9781400882533
    46 https://doi.org/10.1515/crll.2005.2005.581.31
    47 https://doi.org/10.17323/1609-4514-2008-8-1-111-118
    48 https://doi.org/10.4007/annals.2005.162.581
    49 https://doi.org/10.4310/mrl.2003.v10.n2.a5
    50 schema:datePublished 2009-12
    51 schema:datePublishedReg 2009-12-01
    52 schema:description We classify all unitary modular tensor categories (UMTCs) of rank ≤ 4. There are a total of 35 UMTCs of rank ≤ 4 up to ribbon tensor equivalence. Since the distinction between the modular S-matrix S and −S has both topological and physical significance, so in our convention there are a total of 70 UMTCs of rank ≤ 4. In particular, there are two trivial UMTCs with S = (±1). Each such UMTC can be obtained from 10 non-trivial prime UMTCs by direct product, and some symmetry operations. Explicit data of the 10 non-trivial prime UMTCs are given in Sect. 5. Relevance of UMTCs to topological quantum computation and various conjectures are given in Sect. 6.
    53 schema:genre research_article
    54 schema:inLanguage en
    55 schema:isAccessibleForFree true
    56 schema:isPartOf N5578d113b4674926994dbcfba84a3d7d
    57 Nf70599ff0f5443e88299f3af224808eb
    58 sg:journal.1136216
    59 schema:name On Classification of Modular Tensor Categories
    60 schema:pagination 343-389
    61 schema:productId N8ab76ac616c34213a49f0b4ba8581fca
    62 N9e071edb18c94f9e963ec3a91fbe7e62
    63 Nee351ba118884d6fac6a003e58a166a8
    64 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006159661
    65 https://doi.org/10.1007/s00220-009-0908-z
    66 schema:sdDatePublished 2019-04-11T14:29
    67 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    68 schema:sdPublisher Nd7ea4d4482ec4d799973d52a2952a10c
    69 schema:url http://link.springer.com/10.1007%2Fs00220-009-0908-z
    70 sgo:license sg:explorer/license/
    71 sgo:sdDataset articles
    72 rdf:type schema:ScholarlyArticle
    73 N5578d113b4674926994dbcfba84a3d7d schema:volumeNumber 292
    74 rdf:type schema:PublicationVolume
    75 N874654e16df14358b737c6f49c1ca652 schema:name Center for Communications Research, 4320 Westerra Court, 92121-1969, San Diego, CA, U.S.A.
    76 rdf:type schema:Organization
    77 N8ab76ac616c34213a49f0b4ba8581fca schema:name readcube_id
    78 schema:value 1d577c6cc450d0c8635e176ac74f674b710c7d75f910cb6f8194f545710959af
    79 rdf:type schema:PropertyValue
    80 N9e071edb18c94f9e963ec3a91fbe7e62 schema:name dimensions_id
    81 schema:value pub.1006159661
    82 rdf:type schema:PropertyValue
    83 Ncb395cde10014538b17da9b24bad323b rdf:first sg:person.014043620101.93
    84 rdf:rest rdf:nil
    85 Nd7ea4d4482ec4d799973d52a2952a10c schema:name Springer Nature - SN SciGraph project
    86 rdf:type schema:Organization
    87 Ndb89c408336a4d34b8f2a5acd584f7a9 rdf:first sg:person.013246237501.57
    88 rdf:rest Ndddaf7c446ef4178abf838a9a075349a
    89 Ndddaf7c446ef4178abf838a9a075349a rdf:first sg:person.01234166050.20
    90 rdf:rest Ncb395cde10014538b17da9b24bad323b
    91 Nee351ba118884d6fac6a003e58a166a8 schema:name doi
    92 schema:value 10.1007/s00220-009-0908-z
    93 rdf:type schema:PropertyValue
    94 Nf70599ff0f5443e88299f3af224808eb schema:issueNumber 2
    95 rdf:type schema:PublicationIssue
    96 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    97 schema:name Mathematical Sciences
    98 rdf:type schema:DefinedTerm
    99 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    100 schema:name Pure Mathematics
    101 rdf:type schema:DefinedTerm
    102 sg:journal.1136216 schema:issn 0010-3616
    103 1432-0916
    104 schema:name Communications in Mathematical Physics
    105 rdf:type schema:Periodical
    106 sg:person.01234166050.20 schema:affiliation N874654e16df14358b737c6f49c1ca652
    107 schema:familyName Stong
    108 schema:givenName Richard
    109 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01234166050.20
    110 rdf:type schema:Person
    111 sg:person.013246237501.57 schema:affiliation https://www.grid.ac/institutes/grid.264756.4
    112 schema:familyName Rowell
    113 schema:givenName Eric
    114 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013246237501.57
    115 rdf:type schema:Person
    116 sg:person.014043620101.93 schema:affiliation https://www.grid.ac/institutes/grid.133342.4
    117 schema:familyName Wang
    118 schema:givenName Zhenghan
    119 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014043620101.93
    120 rdf:type schema:Person
    121 sg:pub.10.1007/bf01238857 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034666835
    122 https://doi.org/10.1007/bf01238857
    123 rdf:type schema:CreativeWork
    124 sg:pub.10.1007/bf02096860 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049272767
    125 https://doi.org/10.1007/bf02096860
    126 rdf:type schema:CreativeWork
    127 sg:pub.10.1007/bf02096988 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033632840
    128 https://doi.org/10.1007/bf02096988
    129 rdf:type schema:CreativeWork
    130 sg:pub.10.1007/bf02352496 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051824934
    131 https://doi.org/10.1007/bf02352496
    132 rdf:type schema:CreativeWork
    133 sg:pub.10.1007/bfb0084244 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029526220
    134 https://doi.org/10.1007/bfb0084244
    135 rdf:type schema:CreativeWork
    136 sg:pub.10.1007/s002080050011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044599308
    137 https://doi.org/10.1007/s002080050011
    138 rdf:type schema:CreativeWork
    139 sg:pub.10.1007/s00220-005-1382-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1011308383
    140 https://doi.org/10.1007/s00220-005-1382-x
    141 rdf:type schema:CreativeWork
    142 sg:pub.10.1007/s002200200635 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043125022
    143 https://doi.org/10.1007/s002200200635
    144 rdf:type schema:CreativeWork
    145 sg:pub.10.1007/s002200200636 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031600564
    146 https://doi.org/10.1007/s002200200636
    147 rdf:type schema:CreativeWork
    148 sg:pub.10.1007/s002200200645 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006311725
    149 https://doi.org/10.1007/s002200200645
    150 rdf:type schema:CreativeWork
    151 sg:pub.10.1007/s10801-005-2514-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012459886
    152 https://doi.org/10.1007/s10801-005-2514-2
    153 rdf:type schema:CreativeWork
    154 sg:pub.10.1007/s10801-008-0139-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1031435106
    155 https://doi.org/10.1007/s10801-008-0139-y
    156 rdf:type schema:CreativeWork
    157 https://app.dimensions.ai/details/publication/pub.1029526220 schema:CreativeWork
    158 https://app.dimensions.ai/details/publication/pub.1098924973 schema:CreativeWork
    159 https://doi.org/10.1016/0040-9383(92)90015-a schema:sameAs https://app.dimensions.ai/details/publication/pub.1028642877
    160 rdf:type schema:CreativeWork
    161 https://doi.org/10.1016/0370-2693(90)91593-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1003832335
    162 rdf:type schema:CreativeWork
    163 https://doi.org/10.1016/0370-2693(94)91226-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025921751
    164 rdf:type schema:CreativeWork
    165 https://doi.org/10.1016/0370-2693(95)00172-h schema:sameAs https://app.dimensions.ai/details/publication/pub.1019591000
    166 rdf:type schema:CreativeWork
    167 https://doi.org/10.1016/0550-3213(91)90407-o schema:sameAs https://app.dimensions.ai/details/publication/pub.1052458791
    168 rdf:type schema:CreativeWork
    169 https://doi.org/10.1016/j.aop.2005.10.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025107810
    170 rdf:type schema:CreativeWork
    171 https://doi.org/10.1016/s0003-4916(02)00018-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015449553
    172 rdf:type schema:CreativeWork
    173 https://doi.org/10.1016/s0022-4049(02)00248-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049588929
    174 rdf:type schema:CreativeWork
    175 https://doi.org/10.1016/s0370-2693(96)01662-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051813315
    176 rdf:type schema:CreativeWork
    177 https://doi.org/10.1016/s0550-3213(98)00111-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009031292
    178 rdf:type schema:CreativeWork
    179 https://doi.org/10.1063/1.532333 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015354582
    180 rdf:type schema:CreativeWork
    181 https://doi.org/10.1073/pnas.95.1.98 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052652635
    182 rdf:type schema:CreativeWork
    183 https://doi.org/10.1080/00018739500101566 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034510423
    184 rdf:type schema:CreativeWork
    185 https://doi.org/10.1090/advsov/016.2/03 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101567767
    186 rdf:type schema:CreativeWork
    187 https://doi.org/10.1090/conm/413/07848 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089201948
    188 rdf:type schema:CreativeWork
    189 https://doi.org/10.1090/s0273-0979-02-00964-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044082506
    190 rdf:type schema:CreativeWork
    191 https://doi.org/10.1090/s0894-0347-98-00253-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049305288
    192 rdf:type schema:CreativeWork
    193 https://doi.org/10.1098/rsta.1989.0082 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004613370
    194 rdf:type schema:CreativeWork
    195 https://doi.org/10.1103/physreva.75.032322 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009445047
    196 rdf:type schema:CreativeWork
    197 https://doi.org/10.1103/physrevb.71.045110 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047264319
    198 rdf:type schema:CreativeWork
    199 https://doi.org/10.1103/physrevb.77.235108 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044867752
    200 rdf:type schema:CreativeWork
    201 https://doi.org/10.1103/physrevb.78.155109 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053383637
    202 rdf:type schema:CreativeWork
    203 https://doi.org/10.1103/physrevlett.98.160409 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019178285
    204 rdf:type schema:CreativeWork
    205 https://doi.org/10.1103/revmodphys.80.1083 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028121061
    206 rdf:type schema:CreativeWork
    207 https://doi.org/10.1112/s0024611503014187 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049189079
    208 rdf:type schema:CreativeWork
    209 https://doi.org/10.1142/9789812772527_0005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1096058469
    210 rdf:type schema:CreativeWork
    211 https://doi.org/10.1142/s0219199708003162 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062991261
    212 rdf:type schema:CreativeWork
    213 https://doi.org/10.1515/9781400882533 schema:sameAs https://app.dimensions.ai/details/publication/pub.1096910407
    214 rdf:type schema:CreativeWork
    215 https://doi.org/10.1515/crll.2005.2005.581.31 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040019718
    216 rdf:type schema:CreativeWork
    217 https://doi.org/10.17323/1609-4514-2008-8-1-111-118 schema:sameAs https://app.dimensions.ai/details/publication/pub.1111409547
    218 rdf:type schema:CreativeWork
    219 https://doi.org/10.4007/annals.2005.162.581 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071866940
    220 rdf:type schema:CreativeWork
    221 https://doi.org/10.4310/mrl.2003.v10.n2.a5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072462218
    222 rdf:type schema:CreativeWork
    223 https://www.grid.ac/institutes/grid.133342.4 schema:alternateName University of California, Santa Barbara
    224 schema:name Microsoft Station Q, University of California, CNSI Bldg, Rm 2237, 93106-6105, Santa Barbara, CA, U.S.A.
    225 rdf:type schema:Organization
    226 https://www.grid.ac/institutes/grid.264756.4 schema:alternateName Texas A&M University
    227 schema:name Department of Mathematics, Texas A&M University, 77843, College Station, TX, U.S.A.
    228 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...