2009 Fiscal Year Final Research Report
On a derived equivalence classification for blocks of finite groups
| Project/Area Number |
19740018
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
KUNUGI Naoko Tokyo University of Science, 理学部第一部, 講師 (50362306)
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| Project Period (FY) |
2007 – 2009
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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 |
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| 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.
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