Finiteness Condition (Fg) for Self-Injective Koszul Algebras View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-04

AUTHORS

Ayako Itaba

ABSTRACT

Let k be an algebraically closed field. For a graded algebra, Mori introduced a notion of cogeometric pair (E, σ), where E⊂ℙn−1 is a subscheme and σ ∈Aut E. On the other hand, for a finite-dimensional algebra, Erdmann et al. defined the finiteness condition (Fg). In this paper, we show the following results which state relationships between cogeometric pairs and (Fg). Let A=A!(E,σ) be a cogeometric self-injective Koszul k-algebra such that the complexity of k is finite. (1) If A satisfies (Fg), then the order of σ is finite. (2) In the case of E=ℙn−1, A satisfies (Fg) if and only if the order of σ is finite. (3) If A satisfies (rad A)4 = 0, then A satisfies (Fg) if and only if the order of σ is finite. More... »

PAGES

425-435

References to SciGraph publications

  • 1991-12. Modules over regular algebras of dimension 3 in INVENTIONES MATHEMATICAE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10468-018-9775-7

    DOI

    http://dx.doi.org/10.1007/s10468-018-9775-7

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1101267358


    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": "Tokyo University of Science", 
              "id": "https://www.grid.ac/institutes/grid.143643.7", 
              "name": [
                "Department of Mathematics, Faculty of Science, Shizuoka University, 336 Ohya, 422-8529, Shizuoka, Japan", 
                "Department of Mathematics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, 162-8601, Tokyo, Japan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Itaba", 
            "givenName": "Ayako", 
            "id": "sg:person.015530664252.52", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015530664252.52"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1112/s002461150301459x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012038131"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01243916", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020276359", 
              "https://doi.org/10.1007/bf01243916"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jpaa.2010.04.012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024909115"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0021-8693(83)90121-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024993574"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0001-8708(87)90034-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031316152"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1112/s002461070602326x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034807605"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1007/s10977-004-0838-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054523249"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/conm/406/07659", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1089201856"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/9789812774552_0014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1096056632"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-04", 
        "datePublishedReg": "2019-04-01", 
        "description": "Let k be an algebraically closed field. For a graded algebra, Mori introduced a notion of cogeometric pair (E, \u03c3), where E\u2282\u2119n\u22121 is a subscheme and \u03c3 \u2208Aut E. On the other hand, for a finite-dimensional algebra, Erdmann et al. defined the finiteness condition (Fg). In this paper, we show the following results which state relationships between cogeometric pairs and (Fg). Let A=A!(E,\u03c3) be a cogeometric self-injective Koszul k-algebra such that the complexity of k is finite. (1) If A satisfies (Fg), then the order of \u03c3 is finite. (2) In the case of E=\u2119n\u22121, A satisfies (Fg) if and only if the order of \u03c3 is finite. (3) If A satisfies (rad A)4 = 0, then A satisfies (Fg) if and only if the order of \u03c3 is finite.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s10468-018-9775-7", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.6110732", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.6113967", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.5913099", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1136385", 
            "issn": [
              "1386-923X", 
              "1572-9079"
            ], 
            "name": "Algebras and Representation Theory", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "22"
          }
        ], 
        "name": "Finiteness Condition (Fg) for Self-Injective Koszul Algebras", 
        "pagination": "425-435", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "8489fa77661bcd480f0dc58e8cf2fc563c4f395ec7b3a5e68ca520bc8a5383ef"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s10468-018-9775-7"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1101267358"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s10468-018-9775-7", 
          "https://app.dimensions.ai/details/publication/pub.1101267358"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T11:16", 
        "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/v90/0000000354_0000000354/records_11691_00000002.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs10468-018-9775-7"
      }
    ]
     

    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/s10468-018-9775-7'

    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/s10468-018-9775-7'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10468-018-9775-7'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10468-018-9775-7'


     

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

    96 TRIPLES      21 PREDICATES      36 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10468-018-9775-7 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Nd7b1df8edf934bff88be799bb1a31183
    4 schema:citation sg:pub.10.1007/bf01243916
    5 https://doi.org/10.1007/s10977-004-0838-7
    6 https://doi.org/10.1016/0001-8708(87)90034-x
    7 https://doi.org/10.1016/0021-8693(83)90121-7
    8 https://doi.org/10.1016/j.jpaa.2010.04.012
    9 https://doi.org/10.1090/conm/406/07659
    10 https://doi.org/10.1112/s002461070602326x
    11 https://doi.org/10.1112/s002461150301459x
    12 https://doi.org/10.1142/9789812774552_0014
    13 schema:datePublished 2019-04
    14 schema:datePublishedReg 2019-04-01
    15 schema:description Let k be an algebraically closed field. For a graded algebra, Mori introduced a notion of cogeometric pair (E, σ), where E⊂ℙn−1 is a subscheme and σ ∈Aut E. On the other hand, for a finite-dimensional algebra, Erdmann et al. defined the finiteness condition (Fg). In this paper, we show the following results which state relationships between cogeometric pairs and (Fg). Let A=A!(E,σ) be a cogeometric self-injective Koszul k-algebra such that the complexity of k is finite. (1) If A satisfies (Fg), then the order of σ is finite. (2) In the case of E=ℙn−1, A satisfies (Fg) if and only if the order of σ is finite. (3) If A satisfies (rad A)4 = 0, then A satisfies (Fg) if and only if the order of σ is finite.
    16 schema:genre research_article
    17 schema:inLanguage en
    18 schema:isAccessibleForFree false
    19 schema:isPartOf N74e6b84df6054c02bab53adbf75b9f36
    20 Nbf933a4ac62d4e80b44aa694e96b8d59
    21 sg:journal.1136385
    22 schema:name Finiteness Condition (Fg) for Self-Injective Koszul Algebras
    23 schema:pagination 425-435
    24 schema:productId N71560738f4f045c09033edf58b45f52f
    25 Ncfd295da09634d449e9829582064a73f
    26 Nf25f14dd671140eaa1e537c68a5b8628
    27 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101267358
    28 https://doi.org/10.1007/s10468-018-9775-7
    29 schema:sdDatePublished 2019-04-11T11:16
    30 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    31 schema:sdPublisher Nabff0af6ec8b4f8cafb3bdcd536f5e7c
    32 schema:url https://link.springer.com/10.1007%2Fs10468-018-9775-7
    33 sgo:license sg:explorer/license/
    34 sgo:sdDataset articles
    35 rdf:type schema:ScholarlyArticle
    36 N71560738f4f045c09033edf58b45f52f schema:name dimensions_id
    37 schema:value pub.1101267358
    38 rdf:type schema:PropertyValue
    39 N74e6b84df6054c02bab53adbf75b9f36 schema:volumeNumber 22
    40 rdf:type schema:PublicationVolume
    41 Nabff0af6ec8b4f8cafb3bdcd536f5e7c schema:name Springer Nature - SN SciGraph project
    42 rdf:type schema:Organization
    43 Nbf933a4ac62d4e80b44aa694e96b8d59 schema:issueNumber 2
    44 rdf:type schema:PublicationIssue
    45 Ncfd295da09634d449e9829582064a73f schema:name doi
    46 schema:value 10.1007/s10468-018-9775-7
    47 rdf:type schema:PropertyValue
    48 Nd7b1df8edf934bff88be799bb1a31183 rdf:first sg:person.015530664252.52
    49 rdf:rest rdf:nil
    50 Nf25f14dd671140eaa1e537c68a5b8628 schema:name readcube_id
    51 schema:value 8489fa77661bcd480f0dc58e8cf2fc563c4f395ec7b3a5e68ca520bc8a5383ef
    52 rdf:type schema:PropertyValue
    53 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    54 schema:name Mathematical Sciences
    55 rdf:type schema:DefinedTerm
    56 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    57 schema:name Pure Mathematics
    58 rdf:type schema:DefinedTerm
    59 sg:grant.5913099 http://pending.schema.org/fundedItem sg:pub.10.1007/s10468-018-9775-7
    60 rdf:type schema:MonetaryGrant
    61 sg:grant.6110732 http://pending.schema.org/fundedItem sg:pub.10.1007/s10468-018-9775-7
    62 rdf:type schema:MonetaryGrant
    63 sg:grant.6113967 http://pending.schema.org/fundedItem sg:pub.10.1007/s10468-018-9775-7
    64 rdf:type schema:MonetaryGrant
    65 sg:journal.1136385 schema:issn 1386-923X
    66 1572-9079
    67 schema:name Algebras and Representation Theory
    68 rdf:type schema:Periodical
    69 sg:person.015530664252.52 schema:affiliation https://www.grid.ac/institutes/grid.143643.7
    70 schema:familyName Itaba
    71 schema:givenName Ayako
    72 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015530664252.52
    73 rdf:type schema:Person
    74 sg:pub.10.1007/bf01243916 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020276359
    75 https://doi.org/10.1007/bf01243916
    76 rdf:type schema:CreativeWork
    77 https://doi.org/10.1007/s10977-004-0838-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054523249
    78 rdf:type schema:CreativeWork
    79 https://doi.org/10.1016/0001-8708(87)90034-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1031316152
    80 rdf:type schema:CreativeWork
    81 https://doi.org/10.1016/0021-8693(83)90121-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024993574
    82 rdf:type schema:CreativeWork
    83 https://doi.org/10.1016/j.jpaa.2010.04.012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024909115
    84 rdf:type schema:CreativeWork
    85 https://doi.org/10.1090/conm/406/07659 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089201856
    86 rdf:type schema:CreativeWork
    87 https://doi.org/10.1112/s002461070602326x schema:sameAs https://app.dimensions.ai/details/publication/pub.1034807605
    88 rdf:type schema:CreativeWork
    89 https://doi.org/10.1112/s002461150301459x schema:sameAs https://app.dimensions.ai/details/publication/pub.1012038131
    90 rdf:type schema:CreativeWork
    91 https://doi.org/10.1142/9789812774552_0014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1096056632
    92 rdf:type schema:CreativeWork
    93 https://www.grid.ac/institutes/grid.143643.7 schema:alternateName Tokyo University of Science
    94 schema:name Department of Mathematics, Faculty of Science, Shizuoka University, 336 Ohya, 422-8529, Shizuoka, Japan
    95 Department of Mathematics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, 162-8601, Tokyo, Japan
    96 rdf:type schema:Organization
     




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


    ...