• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Applications of Cohomology groups and Shintani descent to Broue's conjecture

Research Project

Project/Area Number 14340012
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionOsaka Kyoiku University (2003-2005)
Osaka University (2002)

Principal Investigator

UNO Katsuhiro  Osaka Kyoiku University, Div.Math.Sci., Prof., 教育学部, 教授 (70176717)

Co-Investigator(Kenkyū-buntansha) KAWANAKA Noriaki  Osaka Univ, Dept.of Pure and Applied Math., Prof., 大学院・情報科学研究科, 教授 (10028219)
HIRAKI Akira  Osaka Kyoiku Univ, Div.Math.Sci., Asso.Prof., 教育学部, 助教授 (90294181)
WAKI Katsushi  Hirosaki Univ., Dept.of Math.System Sci., Asso.Prof., 理工学部, 助教授 (30250591)
HIDA Akihiko  Saitama Univ., Faculty of Education, Asso.Prof., 教育学部, 助教授 (50272274)
KUNUGI Naoko  Aichi Univ.of Education, Faculty of Education, Assistant, 教育学部, 助手 (50362306)
馬場 良始  大阪教育大学, 教育学部, 助教授 (10201724)
奥山 哲郎  北海道教育大学, 教育学部旭川校, 教授 (60128733)
河合 浩明  崇城大学, 工学部, 講師 (10222431)
宇佐美 陽子  お茶の水女子大学, 理学部, 教授 (90151993)
和久井 道久  大阪大学, 大学院・理学研究科, 助手 (60252574)
越谷 重夫  千葉大学, 理学部, 教授 (30125926)
Project Period (FY) 2002 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥10,000,000 (Direct Cost: ¥10,000,000)
Fiscal Year 2005: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2004: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2003: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2002: ¥3,400,000 (Direct Cost: ¥3,400,000)
KeywordsBroue's conjecture / Block algebra / Dade conjecture / Shintani descent / Cohomology group / Perfect isometry / Modular representation / Defect group / コホモロジー / 森田同値 / シュバレー群 / 単純群 / パーフェクト アイソメトリ / 導来同値
Research Abstract

1 (1)For low rank finite Chevalley groups G of type D and F, and for p=5, we constructed a perfect isometry between the principal blocks of G and a Sylow normalizer. We also determine the number of isometries. Moreover, for blocks of cyclic defect groups, we proved that for any bijection between irreducible characters there is a derived equivalence inducing the bijecyion, provided that the local structure of the blocks are the same,
(2)For finite Chevaley groups of type G, and for p=3, we establish certain Morita equivalence between principal blocks for several defining fields.
(3)We proved that Broue's conjecture holds for block with elementary abelian defect groups of order 9.
(4)We have obtained an easy formula for elementary divisors of the Cartan matrices of symmetric groups.
(5)We gave a module theoretic proof for the Mislin's theorem on group fusions.
(6)The fundamental notions of group cohomologies are extended for arbitrary blocks.
2 (1)We extend Dade's conjecture, and check that it holds for many sporadic simple groups and some finte Chevaley groups.
(2)For a block with dihedral defect groups of order eight, we construct functors among the derived categories of normalizers of radical chains which induce the relations between the numbers of simple modules.

Report

(5 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (34 results)

All 2006 2005 2004 2003 Other

All Journal Article (21 results) Book (1 results) Publications (12 results)

  • [Journal Article] On quasi-projective modules and quasi-injective modules2006

    • Author(s)
      Baba Yoshitomo
    • Journal Title

      Scientiae Mathematicae Japonicae 63・1

      Pages: 113-120

    • NAID

      10020293227

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Improving diameter bounds for distance-regular graphs2006

    • Author(s)
      Bang S., Hiraki Akira, Koolen Jack
    • Journal Title

      European J.Combinatorics 27・1

      Pages: 79-89

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Blocks of central p-group extensions2005

    • Author(s)
      S.Koshitani, N.Kunugi
    • Journal Title

      Proceedings of the American Mathematical Society 133

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A generalization of an inequality of Brouwer-Wilbrink2005

    • Author(s)
      Hiraki Akira, Koolen Jack
    • Journal Title

      J.Combinatorial Theory, Ser A 109・1

      Pages: 181-188

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Applications of the retracing method for distance-regular graphs2005

    • Author(s)
      Hiraki Akira
    • Journal Title

      European J.Combinatorics 26・5

      Pages: 717-727

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Blocks of central p-group extensions2005

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

      Proceedings of American Mathematical Society 133・1

      Pages: 21-26

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Note on decomposition Numbers of G2(2^n)2004

    • Author(s)
      K.Waki
    • Journal Title

      Journal of Algebra 274

      Pages: 602-606

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Broue abelian defect group conjecture for the Held group and the sporadic Suzuki group2004

    • Author(s)
      S.Koshitani, N.Kunugi, K.Waki
    • Journal Title

      Journal of Algebra 279

      Pages: 638-666

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Homogeneous systems of parameters in cohomology algebms of finite groups2004

    • Author(s)
      Okuyama Tetsuro, Sasaki Hiroki
    • Journal Title

      Archiv.Math. 82・2

      Pages: 110-121

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A note on decomposition numbers of G_2(2^n)2004

    • Author(s)
      Waki Katsushi
    • Journal Title

      Journal of Algebra 274・2

      Pages: 602-606

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Broue's abelian defect conjecture for the Held group and sporadic Suzuki group2004

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

      Journal of Algebra 279・2

      Pages: 638-666

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The regular polygons of order(S,2)2004

    • Author(s)
      Hiraki Akira, Koolen Jack
    • Journal Title

      Journal of Algebraic Combinatorics 20・2

      Pages: 219-235

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A Higman-Haemers inequality for thick regular near polygons2004

    • Author(s)
      Hiraki Akira, Koolen Jack
    • Journal Title

      Journal of Algebraic Combinatorics 20・2

      Pages: 213-218

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Natural existence proof for Lyons simple group2003

    • Author(s)
      O.Michler, K.Waki, M.Weller
    • Journal Title

      Journal of Algebra and its Applications 2・3

      Pages: 277-315

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Varieties for modules over a block of a finite group,2003

    • Author(s)
      H.Kawai
    • Journal Title

      Osaka Journal of Maththematics 40

      Pages: 327-344

    • NAID

      120004839873

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Natural existence proof for Lyons simple group2003

    • Author(s)
      O.Michler, K.Waki, M.Weller
    • Journal Title

      Journal of Algebra and its Applications 2(3)

      Pages: 277-315

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Varieties for modules over a block of a finite group2003

    • Author(s)
      H.Kawai
    • Journal Title

      Osaka Journal of Maththematics 40

      Pages: 327-344

    • NAID

      120004839873

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Cohomology algebras of blocks of finite groups and Brauer correspondence

    • Author(s)
      H.Kawai, H.Sasaki
    • Journal Title

      Algebras and Representation Theory (掲載予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Cohomology algebras of blocks of finite groups and Brauer correspondence

    • Author(s)
      H.Kawai, H.Sasaki
    • Journal Title

      Algebras and Representation. Theory 2(3)(accepted for publication)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Self-duality of Harada ring of a component type

    • Author(s)
      Baba Yoshitomo
    • Journal Title

      Journal of Algebra and its applications 掲載決定済み

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Algebraic structure of association schemes of prime order

    • Author(s)
      Hanaki Akihide, Uno Katsuhiro
    • Journal Title

      Journal of Algebraic Combinatorics 掲載決定済み

    • Related Report
      2005 Annual Research Report
  • [Book] Representation theory of algebraic groups and quantum groups2004

    • Author(s)
      Shoji Toshiaki, Kawanaka Noriaki他
    • Total Pages
      490
    • Publisher
      Mathematical Society of Japan
    • Related Report
      2004 Annual Research Report
  • [Publications] M.Sawabe, K.Uno: "Conjectures on character degrees for the simple Lyons group"the Quarterly Journal of Mathematics. 54・1. 103-121 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Koshitani, N.Kunugi, K.Waki: "Broue abelian defect group conjecture for Held group and the sporadic Suzuki group"Journal of Algebra. (発表予定).

    • Related Report
      2003 Annual Research Report
  • [Publications] O.Michler, K.Waki, M.Weller: "Natural existence proof for Lyons simple group"Journal of Algebra and its Applications. 2・3. 277-315 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Usami, M.Nakabayashi: "Morita equivalent principal 3-blocks of the Chevalley groups G_2(q)"Proceedings of the London Mathematical Society. 86・2. 397-434 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Kratzer, W.Lempken, O.Michler, K.Waki: "Another existence and uniqueness proof for McLaughlin's simple group"Journal of Group Theory. 6・4. 443-459 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Kawai: "Varieties for modules over a block of a finite group"Osaka Journal of Mathematics. 40.2. 327-344 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Uno Katsuhiro, Yoshida Satoshi: "Dade's conjecture for the simple O'Nan group"Journal of Algebra. 249・1. 445-468 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Sawabe Masato, Uno Katsuhiro: "Conjecture on character degrees for simple Lyons group"Quarterly Journal of Mathematics. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] Uno Katsuhiro: "Conjecture on character degrees for simple Thompson group"Osaka Journal of Mathematics. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] Wakui Michihisa: "Various structures associated to the representation categories of 8-dimensional non-semisimple Hopfalgebras"Algebra and Representation Theory. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] Usami Yoko, Nakabayashi Miyako: "Morita equivalent principal 3-blocks of the chevalley group G_2(q)"Proceedings of London Mathematical Society. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] Koshitani Shigeo, Kunugi Naoko, Waki Katsushi: "Broue's conjecture for non-principal 3-blocks of finite groups"Journal of Pure and Applied Algebra. 173. 177-211 (2002)

    • Related Report
      2002 Annual Research Report

URL: 

Published: 2002-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi