2002 Fiscal Year Final Research Report Summary
Research on Broue's conjecture
| Project/Area Number |
13640033
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kumamoto University |
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Principal Investigator |
WATANABE Atsumi Kumamoto University, Faculty of Science, Professor, 理学部, 助教授 (90040120)
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| Co-Investigator(Kenkyū-buntansha) |
HORIMOTO Hiroshi Kumamoto National College of Technology, Assistant, 助手 (20342587)
SASAKI Hiroki Ehime University, Professor, 理学部, 教授 (60142684)
USAMI Yoko Ochanomizu University, Professor, 理学部, 教授 (90151993)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Broue's conjecture / Isaacs correspondence / block / derived equivalence / Alperin's conjecture / Morita equivalence / perfect isometry |
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| Research Abstract |
1. We showed that a block of a finite group and its Isaacs correspondent are Morita equivalent : Let A and G be finite groups of coprime orders such that A acts on G via automorphims. If B is a A-invariant block of G with a defect group centralized by A, then there exists a block b of C_G(A) such that B and b are perfect isometric by the Isaacs correspondence. B and b are Morita equivalent.This result is to be appeared in Archiv der Mathematik.
2. We also showed that Broue's conjecture for the principal blocks of finite groups under some conditions is reduced to the finite simple groups: Let r be a prime. If Broue's conjecture is true for the principal blocks of finite simple groups G such that N_G(P)/C_G(P) is a cyclic group of order r^2 for an abelian Sylow p-subgroup P of G, then Broue's conjecture is true for the principal blocks of finite groups G such that N_G(P)/C_G(P) is a cyclic group of order r^2 for an abelian Sylow p-subgroup P of G.
3. We showed that blocks of finite general groups are isotypic by Shintani descent under some conditions.
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