A Study on Derived Equivalences of Blocks and Shintani Descent in Group Algebras

群代数中分块导出等价及新谷下降的研究

• 批准号: 16540001
• 负责人: OKUYAMA Tetsuro
• 金额: $ 2.24万
• 依托单位: Hokkaido University of Education
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540001/
• 关键词: Representations of Finite Groups; Block Algebras; Splendid Tilting Complexes; Shintani Descent; Broue's Conjecture

In the research of this project, we studied "the abelian defect conjecture" which is one of main problems in representation theory of finite groups. We were concerned with Shintani descent and Glauberman correspondent.1.We have constructed one sided tilting complexes for finite Chevalley groups of small rank, for example, U(3,q^2)、Sp(4,q)、G_2(q). We could construct Splendid tilting complexes which coincide with these complexes as one side complexes and studied perfect isometries between character rings induced by them.2.The situations described in 1 can be considered problems of derived category version of "Glauberman correspondent". We have studied solvable group case and obtain some generalization of results by Harris and Linckelmann. And we clarify the strategy raised by Rouquier in this setting.3.We also worked on a problem giving quiver presentations for various types of 5-Sylow normalizers of rank 2 to apply for constructing tilting complexes of some finite Chevalley groups, for example, ^2F_4(q) of which 5-Sylow normalizer is of 4S_4-type.

在本项目的研究中，我们研究了有限群表示论中的主要问题之一“阿贝尔亏损猜想”。1.我们构造了小秩有限Chevalley群的单侧倾斜复形，例如U（3，q^2），Sp（4，q），G_2（q）.我们可以构造与这些复形重合的Splendid倾斜复形作为单侧复形，并研究由它们诱导的特征标环之间的完全等距性。2.[1]中描述的情形可以认为是“Glauberman对应”的导出范畴版本问题。研究了可解群的情形，得到了Harris和Linkelmann的一些结果的推广. 3.我们还研究了秩为2的各种类型的5-Sylow正规化子在构造某些有限Chevalley群的倾斜复形中的应用问题，例如，^2F_4（q），其中的5-Sylow正规化子是4S_4-型的.

项目成果

On a theorem of Mislin on cohomology isomorphism and control of fusion

论Mislin上同调同构定理及融合控制

• 发表时间: 2006
• 期刊: 数理解析研究所講究録 1466
• 作者: 高垣忠一朗;春日井敏之編著;梅野正信;T.Okuyama
• 通讯作者: T.Okuyama

Subspaces given by a projective Randers changedeals in regular local rings

投影 Randers 给出的子空间改变了常规局部环中的值

• 发表时间: 2005
• 期刊: Tensor N.S. 66
• 作者: J.H.Keum;K.Oguiso;D.-θ.Zhang;K.Oguiso;M.Kitayama
• 通讯作者: M.Kitayama

Gorenstein graded rings associated to ideals

Gorenstein 对与理想相关的戒指进行分级

• 发表时间: 2005
• 期刊: J. Algebra 294
• 作者: S.Goto;S.Goto
• 通讯作者: S.Goto

Infinitesimal holomorphically projectice transformation on tnagent bundles with complete lift

具有完全升力的tnagent丛上的无穷小全纯投影变换

• 发表时间: 2005
• 期刊: Differential Geometry-Dynamical Systems 7
• 作者: I.Hasegawa;K.Yamaguchi
• 通讯作者: K.Yamaguchi

Hypersurfaces given by a projective Randers change

由投影 Randers 变化给出的超曲面

• 发表时间: 2005
• 期刊: Proceedings of International Workshop Applied Mathematics, Banat's University, Romania,
• 作者: M.Kitayama;T.Tani
• 通讯作者: T.Tani