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Modular and integral representations of finite groups and algebras

Research Project

Project/Area Number 19540044
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionOsaka City University

Principal Investigator

KAWATA Shigeto  Osaka City University, 大学院・理学研究科, 准教授 (50195103)

Co-Investigator(Kenkyū-buntansha) 兼田 正治  大阪市立大学, 大学院・理学研究科, 教授 (60204575)
住岡 武  大阪市立大学, 大学院・理学研究科, 准教授 (90047366)
加戸 次郎  大阪市立大学, 大学院・理学研究科, 講師 (10117939)
浅芝 秀人  静岡大学, 理学部, 教授 (70175165)
Co-Investigator(Renkei-kenkyūsha) KANEDA Masaharu  大阪市立大学, 大学院・理学研究科, 教授 (60204575)
ASASHIBA Hideto  静岡大学, 理学部, 教授 (70175165)
KADO Jiro  大阪市立大学, 大学院・理学研究科, 講師 (10117939)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords表現論 / 有限群 / 群環 / 多元環 / 概分裂列 / Auslander-Reiten有向グラフ / Auslander-Reitn有向グラフ / 表現
Research Abstract

We gave a proof of the indecomposability for certain Heller lattices over integral group rings. Also, we investigated the Auslander-Reiten quiver of an integral group ring, and we showed that Auslander-Reiten components containing trivial source lattices belonging to a block of infinite representation type are of type A-infinity and trivial source lattices lie at the end of their components.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (26 results)

All 2010 2009 2008 2007

All Journal Article (14 results) (of which Peer Reviewed: 11 results) Presentation (12 results)

  • [Journal Article] On Auslander-Reiten components and trivial source lattices for integral group rings2009

    • Author(s)
      河田成人
    • Journal Title

      Journal of Algebra 322

      Pages: 1395-1405

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The structure of Humphreys-Verma modules for projective spaces2009

    • Author(s)
      Masaharu Kaneda
    • Journal Title

      Journal of Algebra 322

      Pages: 237-244

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Auslander-Reiten components and trivial source lattices for integral group rings2009

    • Author(s)
      Shigeto Kawata
    • Journal Title

      Journal of Algebra 322

      Pages: 1395-1405

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On Auslander Reiten components and trivial source lattices for integral group rings2009

    • Author(s)
      Shigeto Kawata
    • Journal Title

      Journal of Algebra 322

      Pages: 1395-1405

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Kapranov's tilting sheaf on the Grassmannian in positive characteristic2008

    • Author(s)
      Kaneda Masaharu
    • Journal Title

      Algebras and Representation Theory 11

      Pages: 347-354

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Domestic canonical algebras and simple Lie algebras2008

    • Author(s)
      Asashiba Hideto
    • Journal Title

      Mathematische Zeitschrift 259

      Pages: 713-754

    • NAID

      120001794399

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Erratum to "On Heller lattices over ramified extended orders"2008

    • Author(s)
      河田成人
    • Journal Title

      Journal of Pure and Applied Algebra 212

      Pages: 1849-1851

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Erratum to "On Heller lattices over ramified extended orders"2008

    • Author(s)
      Shigeto Kawata
    • Journal Title

      Journal of Pure and Applied Algebra 212

      Pages: 1849-1851

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Erratum to“On Heller lattices over ramified extended orders"2008

    • Author(s)
      Shigeto Kawata
    • Journal Title

      Journal of Pure and Applied Algebra 212

      Pages: 1849-1851

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Equivariant localization of D-modules on the flag variety of the symplectic group of degree 42007

    • Author(s)
      Kaneda Masaharu, Ye Jiachen
    • Journal Title

      Journal of Algebra 309

      Pages: 236-281

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 群環のHeller格子について2007

    • Author(s)
      河田成人
    • Journal Title

      数理解析研究所講究録 1564

      Pages: 70-75

    • Related Report
      2010 Final Research Report
  • [Journal Article] 群環の Heller 格子について2007

    • Author(s)
      河田成人
    • Journal Title

      数理解析研究所講究録 1564

      Pages: 70-75

    • Related Report
      2009 Self-evaluation Report
  • [Journal Article] 群環のHeller格子について2007

    • Author(s)
      河田 成人
    • Journal Title

      数理解析研究所講究録 1564

      Pages: 70-75

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Equivariant localization of D-modules on the flag variety of the symplectic group of degree 42007

    • Author(s)
      Kaneda M. and Ye, J.
    • Journal Title

      J.Algebra 309

      Pages: 236-281

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] 群環におけるAuslander-Reiten成分とトレース写像が分裂する加群について2010

    • Author(s)
      河田成人
    • Organizer
      2010年度日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-22
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Some observations on the structure of F_*O_<G/P>2010

    • Author(s)
      兼田正治
    • Organizer
      Representation Theory of Algebraic Groups and Quantum Groups(第10回名古屋国際数学コンファレンス)
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-08-06
    • Related Report
      2010 Final Research Report
  • [Presentation] The 2-categories of G-categories and of G-graded categories are 2-equivalent for any group G2009

    • Author(s)
      浅芝秀人
    • Organizer
      2009年度日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2010 Final Research Report
  • [Presentation] 群環の自明なソースを持つ加群とAuslander-Reiten quivers2009

    • Author(s)
      河田成人
    • Organizer
      2009年度日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] 群環の自明なソースを持つ加群と Auslander-Reiten quivers2009

    • Author(s)
      河田成人
    • Organizer
      2009年度日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Auslander-Reiten components and trivial source modules for integral group rings2009

    • Author(s)
      河田成人
    • Organizer
      表現論セミナー
    • Place of Presentation
      信州大学
    • Year and Date
      2009-02-21
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report 2008 Annual Research Report
  • [Presentation] On Auslander-Reiten components of type A-infinity for integral group rings2008

    • Author(s)
      河田成人
    • Organizer
      Algebra Seminar
    • Place of Presentation
      大阪府立大学
    • Year and Date
      2008-12-17
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report 2008 Annual Research Report
  • [Presentation] Covering functors, orbit categories and derived equivalences2007

    • Author(s)
      浅芝秀人
    • Organizer
      XII International Conference on Representation Theory and Algebras(第12回多元環の表現論国際会議)
    • Place of Presentation
      NicolausCopernicus University(ニコラウス・コペルニクス大学、トルン、ポーランド)
    • Year and Date
      2007-08-23
    • Related Report
      2010 Final Research Report
  • [Presentation] Heller lattices and Auslander-Reiten quivers for integral group rings2007

    • Author(s)
      河田成人
    • Organizer
      XII International Conference on Representation Theory and Algebras(第12回多元環の表現論国際会議)
    • Place of Presentation
      Nicolaus Copernicus University(ニコラウス・コペルニクス大学、トルン、ポーランド)
    • Year and Date
      2007-08-23
    • Related Report
      2010 Final Research Report
  • [Presentation] Heller lattices and Auslander-Reiten quivers for integral group rings2007

    • Author(s)
      Shigeto Kawata
    • Organizer
      第12回多元環の表現論国際会議
    • Place of Presentation
      ニコラウス・コペルニクス大学 (トルン, ポーランド)
    • Year and Date
      2007-08-23
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Heller lattices and Auslander-Reiten quivers for integral group rings2007

    • Author(s)
      河田 成人
    • Organizer
      第12回多元環の表現論国際会議
    • Place of Presentation
      ニコラウス・コペルニクス大学トルン,ポーランド
    • Year and Date
      2007-08-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Covering functors,orbit categories and derived equivalences2007

    • Author(s)
      浅芝 秀人
    • Organizer
      第12回多元環の表現論国際会議
    • Place of Presentation
      ニコラウス・コペルニクス大学トルン,ポーランド
    • Year and Date
      2007-08-23
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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