Canonical bases and Hall algebras View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1998

AUTHORS

George Lusztig

ABSTRACT

In these lectures we discuss the canonical basis of the plus part of the q-analogue of the enveloping algebra of a semisimple Lie algebra. The main emphasis is on the description of this basis in the framework of Hall algebras, that is, in terms of functions on the moduli space of representations of a quiver. We also give an interpretation of the action of the braid group in terms of Hall algebras. More... »

PAGES

365-399

References to SciGraph publications

  • 1980-12. La Conjecture de Weil. II in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 1990-12. Hall algebras and quantum groups in INVENTIONES MATHEMATICAE
  • 1992-12. Affine quivers and canonical bases in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 1995-12. Hall algebras, hereditary algebras and quantum groups in INVENTIONES MATHEMATICAE
  • Book

    TITLE

    Representation Theories and Algebraic Geometry

    ISBN

    978-90-481-5075-5
    978-94-015-9131-7

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-94-015-9131-7_9

    DOI

    http://dx.doi.org/10.1007/978-94-015-9131-7_9

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1027192115


    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": "Massachusetts Institute of Technology", 
              "id": "https://www.grid.ac/institutes/grid.116068.8", 
              "name": [
                "Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA\u00a002139, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Lusztig", 
            "givenName": "George", 
            "id": "sg:person.01042271770.43", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01042271770.43"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf02699432", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005545204", 
              "https://doi.org/10.1007/bf02699432"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1073/pnas.89.17.8177", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024306081"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0894-0347-1990-1035415-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027548652"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01231516", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040141253", 
              "https://doi.org/10.1007/bf01231516"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01231516", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040141253", 
              "https://doi.org/10.1007/bf01231516"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01241133", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043262539", 
              "https://doi.org/10.1007/bf01241133"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02684780", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051562332", 
              "https://doi.org/10.1007/bf02684780"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0894-0347-1991-1088333-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053506412"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/s0012-7094-91-06321-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064419691"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1998", 
        "datePublishedReg": "1998-01-01", 
        "description": "In these lectures we discuss the canonical basis of the plus part of the q-analogue of the enveloping algebra of a semisimple Lie algebra. The main emphasis is on the description of this basis in the framework of Hall algebras, that is, in terms of functions on the moduli space of representations of a quiver. We also give an interpretation of the action of the braid group in terms of Hall algebras.", 
        "editor": [
          {
            "familyName": "Broer", 
            "givenName": "Abraham", 
            "type": "Person"
          }, 
          {
            "familyName": "Daigneault", 
            "givenName": "A.", 
            "type": "Person"
          }, 
          {
            "familyName": "Sabidussi", 
            "givenName": "Gert", 
            "type": "Person"
          }
        ], 
        "genre": "chapter", 
        "id": "sg:pub.10.1007/978-94-015-9131-7_9", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": {
          "isbn": [
            "978-90-481-5075-5", 
            "978-94-015-9131-7"
          ], 
          "name": "Representation Theories and Algebraic Geometry", 
          "type": "Book"
        }, 
        "name": "Canonical bases and Hall algebras", 
        "pagination": "365-399", 
        "productId": [
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/978-94-015-9131-7_9"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "81882830b5e5f4a5d79a222bf733fac1cac65237eef6e9f7c180109e185b17a3"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1027192115"
            ]
          }
        ], 
        "publisher": {
          "location": "Dordrecht", 
          "name": "Springer Netherlands", 
          "type": "Organisation"
        }, 
        "sameAs": [
          "https://doi.org/10.1007/978-94-015-9131-7_9", 
          "https://app.dimensions.ai/details/publication/pub.1027192115"
        ], 
        "sdDataset": "chapters", 
        "sdDatePublished": "2019-04-15T12:32", 
        "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/v90/0000000001_0000000264/records_8663_00000260.jsonl", 
        "type": "Chapter", 
        "url": "http://link.springer.com/10.1007/978-94-015-9131-7_9"
      }
    ]
     

    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.10.1007/978-94-015-9131-7_9'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-94-015-9131-7_9'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-94-015-9131-7_9'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-94-015-9131-7_9'


     

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

    103 TRIPLES      23 PREDICATES      35 URIs      20 LITERALS      8 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/978-94-015-9131-7_9 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N78cec821b4e44200a5909db8e7519630
    4 schema:citation sg:pub.10.1007/bf01231516
    5 sg:pub.10.1007/bf01241133
    6 sg:pub.10.1007/bf02684780
    7 sg:pub.10.1007/bf02699432
    8 https://doi.org/10.1073/pnas.89.17.8177
    9 https://doi.org/10.1090/s0894-0347-1990-1035415-6
    10 https://doi.org/10.1090/s0894-0347-1991-1088333-2
    11 https://doi.org/10.1215/s0012-7094-91-06321-0
    12 schema:datePublished 1998
    13 schema:datePublishedReg 1998-01-01
    14 schema:description In these lectures we discuss the canonical basis of the plus part of the q-analogue of the enveloping algebra of a semisimple Lie algebra. The main emphasis is on the description of this basis in the framework of Hall algebras, that is, in terms of functions on the moduli space of representations of a quiver. We also give an interpretation of the action of the braid group in terms of Hall algebras.
    15 schema:editor N1556f008f0a145329e0cad63eb785f49
    16 schema:genre chapter
    17 schema:inLanguage en
    18 schema:isAccessibleForFree false
    19 schema:isPartOf Nc1bd33903ff74f3b92d9c152363814ba
    20 schema:name Canonical bases and Hall algebras
    21 schema:pagination 365-399
    22 schema:productId N600c9e93f2aa4b90b396375c11727df7
    23 N60eb9bc2ac034b22838c67c5695041d6
    24 Naa4b413cca294bef849f174b286b4b01
    25 schema:publisher N15c702de75134b57a185fac49f871e05
    26 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027192115
    27 https://doi.org/10.1007/978-94-015-9131-7_9
    28 schema:sdDatePublished 2019-04-15T12:32
    29 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    30 schema:sdPublisher Nebdeabb0fd814954934ad6c2616a3936
    31 schema:url http://link.springer.com/10.1007/978-94-015-9131-7_9
    32 sgo:license sg:explorer/license/
    33 sgo:sdDataset chapters
    34 rdf:type schema:Chapter
    35 N1556f008f0a145329e0cad63eb785f49 rdf:first N90180caf20ae4b8a965b3d94b29b2434
    36 rdf:rest N79f459eab2ca4ed7b54d6e3b6b105193
    37 N15c702de75134b57a185fac49f871e05 schema:location Dordrecht
    38 schema:name Springer Netherlands
    39 rdf:type schema:Organisation
    40 N600c9e93f2aa4b90b396375c11727df7 schema:name doi
    41 schema:value 10.1007/978-94-015-9131-7_9
    42 rdf:type schema:PropertyValue
    43 N60eb9bc2ac034b22838c67c5695041d6 schema:name readcube_id
    44 schema:value 81882830b5e5f4a5d79a222bf733fac1cac65237eef6e9f7c180109e185b17a3
    45 rdf:type schema:PropertyValue
    46 N78cec821b4e44200a5909db8e7519630 rdf:first sg:person.01042271770.43
    47 rdf:rest rdf:nil
    48 N79f459eab2ca4ed7b54d6e3b6b105193 rdf:first Ne45f334d7aeb4368a67c9fa9c628d58b
    49 rdf:rest Ndd2ccf65b98c442fb9edc3a205da43c6
    50 N90180caf20ae4b8a965b3d94b29b2434 schema:familyName Broer
    51 schema:givenName Abraham
    52 rdf:type schema:Person
    53 Naa4b413cca294bef849f174b286b4b01 schema:name dimensions_id
    54 schema:value pub.1027192115
    55 rdf:type schema:PropertyValue
    56 Nc1bd33903ff74f3b92d9c152363814ba schema:isbn 978-90-481-5075-5
    57 978-94-015-9131-7
    58 schema:name Representation Theories and Algebraic Geometry
    59 rdf:type schema:Book
    60 Ndd2ccf65b98c442fb9edc3a205da43c6 rdf:first Ndf974a8dd910405b989f53d289dea439
    61 rdf:rest rdf:nil
    62 Ndf974a8dd910405b989f53d289dea439 schema:familyName Sabidussi
    63 schema:givenName Gert
    64 rdf:type schema:Person
    65 Ne45f334d7aeb4368a67c9fa9c628d58b schema:familyName Daigneault
    66 schema:givenName A.
    67 rdf:type schema:Person
    68 Nebdeabb0fd814954934ad6c2616a3936 schema:name Springer Nature - SN SciGraph project
    69 rdf:type schema:Organization
    70 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    71 schema:name Mathematical Sciences
    72 rdf:type schema:DefinedTerm
    73 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    74 schema:name Pure Mathematics
    75 rdf:type schema:DefinedTerm
    76 sg:person.01042271770.43 schema:affiliation https://www.grid.ac/institutes/grid.116068.8
    77 schema:familyName Lusztig
    78 schema:givenName George
    79 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01042271770.43
    80 rdf:type schema:Person
    81 sg:pub.10.1007/bf01231516 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040141253
    82 https://doi.org/10.1007/bf01231516
    83 rdf:type schema:CreativeWork
    84 sg:pub.10.1007/bf01241133 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043262539
    85 https://doi.org/10.1007/bf01241133
    86 rdf:type schema:CreativeWork
    87 sg:pub.10.1007/bf02684780 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051562332
    88 https://doi.org/10.1007/bf02684780
    89 rdf:type schema:CreativeWork
    90 sg:pub.10.1007/bf02699432 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005545204
    91 https://doi.org/10.1007/bf02699432
    92 rdf:type schema:CreativeWork
    93 https://doi.org/10.1073/pnas.89.17.8177 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024306081
    94 rdf:type schema:CreativeWork
    95 https://doi.org/10.1090/s0894-0347-1990-1035415-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027548652
    96 rdf:type schema:CreativeWork
    97 https://doi.org/10.1090/s0894-0347-1991-1088333-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053506412
    98 rdf:type schema:CreativeWork
    99 https://doi.org/10.1215/s0012-7094-91-06321-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064419691
    100 rdf:type schema:CreativeWork
    101 https://www.grid.ac/institutes/grid.116068.8 schema:alternateName Massachusetts Institute of Technology
    102 schema:name Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    103 rdf:type schema:Organization
     




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


    ...