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On a derived equivalence classification for blocks of finite groups

Research Project

Project/Area Number 19740018
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionTokyo University of Science

Principal Investigator

KUNUGI Naoko  Tokyo University of Science, 理学部第一部, 講師 (50362306)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,340,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords有限群 / モジュラー表現 / ブロック / 森田同値 / 導来同値 / 安定同値 / プロック
Research Abstract

Broue's abelian defect group conjecture is one of the most important problems in modular representation theory of finite groups. The conjecture states that a block of a finite group with abelian defect group would be derived equivalent to its Brauer correspondent block. In this project, I calculated some examples for the conjecture and try to generalize such results. I also had some results for trivial source modules, which are important for constructing stable equivalences, calculating modules of images of simple modules under the stable equivalences.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (27 results)

All 2010 2009 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 10 results) Presentation (14 results)

  • [Journal Article] Trivial source modules in blocks with cyclic defect group2010

    • Author(s)
      Shigeo Koshitani, Naoko Kunugi
    • Journal Title

      Mathematische Zeitschrift

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Blocks with nonabelian defect groups which have cyclic subgroups of index p2010

    • Author(s)
      Shigeo Koshitani, Naoko Kunugi, Miles Holloway
    • Journal Title

      Archiv der Mathematik

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Blocks with nonabelian defect groups which have cyclic subgroups of index p2010

    • Author(s)
      Miles Holloway, Shigeo Koshitani, Naoko Kunugi
    • Journal Title

      Archiv der Mathematik 94

      Pages: 101-116

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Broue's Abelian defect group conjecture holds for the Janko simple group J_42008

    • Author(s)
      Shigeo Koshitani, Naoko Kunugi, Katsushi Waki
    • Journal Title

      Journal of Pure and Applied Algebra 212巻

      Pages: 1438-1456

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Eigenvalues of Cartan matrices of principal 2-blocks with abelian defect groups2008

    • Author(s)
      Naoko Kunugi, Tomoyuki Wada
    • Journal Title

      Journal of Algebra 319巻

      Pages: 4404-4411

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 可換2-シロー部分群をもつ群における主ブロックのカルタン行列の固有値2008

    • Author(s)
      功刀直子, 和田倶幸
    • Journal Title

      第25回代数的組合せ論シンポジウム報告集

    • Related Report
      2009 Final Research Report
  • [Journal Article] 有限群の表現論におけるブルエ予想2008

    • Author(s)
      功刀直子
    • Journal Title

      第53回代数学シンポジウム報告集

      Pages: 55-66

    • Related Report
      2009 Final Research Report
  • [Journal Article] Broue's abelian defect group conjecture holds for the Janko simple group J42008

    • Author(s)
      Shigeo Koshitani, Naoko Kunugi Katsushi Waki
    • Journal Title

      Journal of Pure and Applied Algebra 212

      Pages: 1438-1456

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Eigenvalues of Caftan matrices of principal 2-blocks with abelian defect groups2008

    • Author(s)
      Naoko Kunugi, Tomoyuki Wada
    • Journal Title

      Journal of Algebra 319

      Pages: 4404-4411

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Broue's Abelian Defect Group Conjecture holds for the Janko simple group J42008

    • Author(s)
      Shigeo Koshitani, Naoko kunugi, Katsushi Waki
    • Journal Title

      Journal of Pure and Applied Algebra 212

      Pages: 1438-1456

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Eigenvalues of Cartan matrices of principal 2-blocks with abelian defect groups2008

    • Author(s)
      Naoko Kunugi, Tomoyuki Wada
    • Journal Title

      Journal of Algebra 319

      Pages: 4404-4411

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] rivial source modules in blocks with cyclic defect groups2007

    • Author(s)
      功刀直子
    • Journal Title

      京都大学数理解析研究所講究録 1564巻

      Pages: 52-57

    • Related Report
      2009 Final Research Report
  • [Journal Article] Trivial source modules in blocks with cyclic defect group

    • Author(s)
      Koshitani Shigeo, Naoko Kunugi
    • Journal Title

      Mathematische Zeitschrift (掲載予定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Scott modules and equivalences between blocks of finite groups2010

    • Author(s)
      功刀直子
    • Organizer
      アバディーン大学代数セミナー
    • Place of Presentation
      アバディーン大学
    • Year and Date
      2010-03-18
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] Morita equivalent blocks of general linear groups in non-defining characteristic2009

    • Author(s)
      功刀直子
    • Organizer
      RIMS研究集会「代数的組合せ論および関連する群と代数」
    • Place of Presentation
      信州大学
    • Year and Date
      2009-11-20
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] 一般線型群の主ブロックの森田同値2009

    • Author(s)
      功刀直子
    • Organizer
      RIMS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 2009 Final Research Report
  • [Presentation] Morita equivalences for general linear groups in non-defining characteristic2009

    • Author(s)
      功刀直子
    • Organizer
      RIMS研究集会「代数的三角圏とその周辺」
    • Place of Presentation
      京都大学
    • Year and Date
      2009-07-22
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] 巡回不足群をもつ有限群のブロックにおける自明なソースをもつ加群2009

    • Author(s)
      功刀直子, 越谷重夫
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学
    • Related Report
      2009 Final Research Report
  • [Presentation] 有限群の表現論における離散的有限単純群J4に対してのブルエ予想2008

    • Author(s)
      功刀直子, 越谷重夫, 脇克志
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学.
    • Year and Date
      2008-09-24
    • Related Report
      2009 Final Research Report
  • [Presentation] Eigenvalues of Cartan matrices of principal 2-blocks with abelian defect groups2008

    • Author(s)
      功刀直子, 和田倶幸
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2009 Final Research Report
  • [Presentation] Derived equivalences for blocks of finite groups having normal subgroups of index p2008

    • Author(s)
      功刀 直子
    • Organizer
      RIMS 研究集会「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
      2008-08-28
    • Related Report
      2007 Annual Research Report
  • [Presentation] 有限群の表現論におけるブルエ予想2008

    • Author(s)
      功刀直子
    • Organizer
      第53回代数学シンポジウム
    • Place of Presentation
      いわて県民情報交流センター
    • Year and Date
      2008-08-05
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] 可換2-シロー部分群をもつ群における主ブロックのカルタン行列の固有値2008

    • Author(s)
      功刀直子, 和田倶幸
    • Organizer
      第25回代数的組合せ論シンポジウム
    • Place of Presentation
      北海道大学
    • Year and Date
      2008-06-24
    • Related Report
      2009 Final Research Report
  • [Presentation] Derived equivalences for blocks with defect groups having cyclic subgroups of index p2008

    • Author(s)
      功刀直子
    • Organizer
      UCSC Algebra Seminar
    • Place of Presentation
      University of California Santa Cruz.
    • Year and Date
      2008-02-01
    • Related Report
      2009 Final Research Report
  • [Presentation] On Broue's abelian defect group conjecture in representation theory of finite groups2007

    • Author(s)
      功刀直子
    • Organizer
      第5回日・中・韓・環論国際シンポジウム
    • Place of Presentation
      国立オリンピック記念青少年総合センター
    • Year and Date
      2007-09-13
    • Related Report
      2009 Final Research Report
  • [Presentation] On Broue's abelina defect group conjecture in representation theory of finite groups2007

    • Author(s)
      Naoko Kunugi
    • Organizer
      第5回日・中・韓・環論国際シンポジューム
    • Place of Presentation
      国立オリンピック記念青少年総合センター
    • Year and Date
      2007-09-13
    • Related Report
      2007 Annual Research Report
  • [Presentation] Derived equivalences for blocks of finite groups having normal subgroups of index p2007

    • Author(s)
      功刀直子
    • 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
      2007-08-28
    • Related Report
      2009 Final Research Report

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

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