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

上同调群和 Shintani 下降在 Broue 猜想中的应用

基本信息

项目摘要

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.
1(1)对于D和F型的低阶有限Chvalley群G,当p=5时,我们构造了G的主块与Sylow正规化子之间的完美等距。我们还确定了等轴测线的数目。此外,对于循环亏群的块,我们证明了对于任何不可约特征标之间的双射,只要块的局部结构相同,(2)对于有限的G型Chvaley群,对于p=3,(3)证明了Broue猜想对具有9阶初等交换亏群的块成立。(4)得到了对称群的Cartan矩阵的初等因子的一个简单公式。(5)给出了关于群融合的Mislin定理的模理论证明。(6)将群上同调的基本概念推广到任意块。2(1)我们推广了Dade猜想,并证明了它对许多零星单群和一些有限Chvaley群都成立。(2)对于具有8阶二面体亏群的块,我们在根链的正规化子的派生范畴之间构造函子,从而导出单模的个数之间的关系。

项目成果

期刊论文数量(34)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
A Higman-Haemers Inequality for Thick Regular Near Polygons
  • DOI:
    10.1023/b:jaco.0000047283.91464.3c
  • 发表时间:
    2004-09
  • 期刊:
  • 影响因子:
    0.8
  • 作者:
    Akira Hiraki;J. Koolen
  • 通讯作者:
    Akira Hiraki;J. Koolen
Sawabe Masato, Uno Katsuhiro: "Conjecture on character degrees for simple Lyons group"Quarterly Journal of Mathematics. (発表予定).
泽部正人,宇野胜宏:“简单里昂群的特征度猜想”数学季刊(待出版)。
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    0
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Self-duality of Harada ring of a component type
组件型原田环的自对偶性
  • DOI:
  • 发表时间:
    2008
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Mourougane Ch.;Takayama Shigeharu;Yoshitomo Baba
  • 通讯作者:
    Yoshitomo Baba
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)
M.Kratzer、W.Lempken、O.Michler、K.Waki:“McLaughlin 简单群的另一个存在性和唯一性证明”群论杂志 6・4(2003 年)。
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    0
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Wakui Michihisa: "Various structures associated to the representation categories of 8-dimensional non-semisimple Hopfalgebras"Algebra and Representation Theory. (発表予定).
Wakui Michihisa:“与 8 维非半简单 Hopfalgebras 的表示类别相关的各种结构”代数和表示理论(待提交)。
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UNO Katsuhiro其他文献

UNO Katsuhiro的其他文献

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{{ truncateString('UNO Katsuhiro', 18)}}的其他基金

Structure of the derived categories of block algebras with non-commutative defect groups
具有非交换缺陷群的分块代数的派生范畴的结构
  • 批准号:
    18540031
  • 财政年份:
    2006
  • 资助金额:
    $ 6.4万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Application of Shintani descent to the perfect isometry problem and Dade's conjecture
Shintani下降在完美等距问题中的应用及Dade猜想
  • 批准号:
    11440008
  • 财政年份:
    1999
  • 资助金额:
    $ 6.4万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
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