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Cohomology of finite groups from the view point of representation theory

Research Project

Project/Area Number 21540007
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionSaitama University

Principal Investigator

HIDA Akihiko  埼玉大学, 教育学部, 准教授 (50272274)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2010: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2009: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Keywords有限群 / 表現論 / コホモロジー / 代数学 / バーンサイド環 / fusion / Burnside環 / 有限次元多元環 / ブロックイデアル / fusion system / 加群の多様体
Research Abstract

We studied the cohomology theory of finite groups and finite dimensional algebras using methods of representation theory. We considered the varieties of modules defined by Hochschild cohomology and the rank varieties of modules over exterior algebras or graded Hopf algebras. In particular, we obtained some results on tensor products of modules. On the other hand, we studied the action of double Burnside algebra on the mod-p cohomology algebra of a finite group and obtained some results on composition factors.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (9 results)

All 2011 2010 2009

All Journal Article (5 results) (of which Peer Reviewed: 3 results) Presentation (4 results)

  • [Journal Article] Module correspondences in Rouquier blocks of finite general linear groups, in Representation Theory of Algebraic groups and Quantum groups2010

    • Author(s)
      飛田明彦, 宮地兵衛
    • Journal Title

      Progressin Mathematics

      Volume: 284 Pages: 82-92

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 有限群のコホモロジー論2010

    • Author(s)
      奥山哲郎, 佐々木洋城, 飛田明彦
    • Journal Title

      数学

      Volume: 62 Pages: 240-266

    • NAID

      10026792732

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Varieties of modules forsome selfinjective algebras2010

    • Author(s)
      飛田明彦
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1679 Pages: 33-43

    • Related Report
      2011 Final Research Report
  • [Journal Article] Module correspondences in Rouquier blocks of finite general linear groups2010

    • Author(s)
      A Hida, H.Miyachi
    • Journal Title

      Progress in Mathematics

      Volume: 284 Pages: 81-92

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Varieties of modules for finite groups and finite dimensional algebras2009

    • Author(s)
      飛田明彦
    • Journal Title

      第54回代数学シンポジウム報告集

      Pages: 65-76

    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Presentation] 有限群の両側Burnside環の表現論2011

    • Author(s)
      飛田明彦
    • Organizer
      有限群のコホモロジー論とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-08-31
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] 自己移入的多元環上の加群の多様体について2009

    • Author(s)
      飛田明彦
    • Organizer
      有限群のコホモロジー論とその周辺
    • Place of Presentation
      信州大学
    • Year and Date
      2009-09-01
    • Related Report
      2011 Final Research Report
  • [Presentation] 自己移入的多元環上の加群の多様体について2009

    • Author(s)
      飛田明彦
    • Organizer
      研究集会有限群のコホモロジー論とその周辺
    • Place of Presentation
      信州大学
    • Year and Date
      2009-09-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] Varieties of modules for finite groups and finite dimensional algebras2009

    • Author(s)
      飛田明彦
    • Organizer
      第54回代数学シンポジウム
    • Place of Presentation
      明治大学
    • Year and Date
      2009-08-03
    • Related Report
      2011 Final Research Report 2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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