2014 Fiscal Year Final Research Report
On equivalences for module categories and their derived categories for blocks of finite groups
Project/Area Number |
22740025
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
Algebra
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Research Institution | Tokyo University of Science |
Principal Investigator |
KUNUGI Naoko 東京理科大学, 理学部, 准教授 (50362306)
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Project Period (FY) |
2010-04-01 – 2015-03-31
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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 |
Outline of Final Research Achievements |
One of the important conjectures in modular representation theory of finite groups is Broue's abelian defect group conjecture. It states that the principal blocks of two finite groups having a common abelian Sylow subgroup and the same fusion systems on the Sylow subgroup should be derived equivalent.To solve the conjecture it is important to develope the way of gluing local derived equivalences to global stable equivalences and of lifting stable equivalences to derived equivalences. In this project, related to gluing processes I obtained a result for Brauer indecomposability of Scott modules with abelian vertex, and then generalize this result to non-abelian vertex case. I also tried to apply these results to obtain new examples of derived equivalences with non-abelian defect groups and Morita equivalences for infinite series of finite groups.
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Free Research Field |
代数学
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