2003 Fiscal Year Final Research Report Summary
A Study on Constructions of Splendid Tilting Complexes and Broue's Conjecture
| Project/Area Number |
14540001
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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 | Hokkaido University of Education |
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Principal Investigator |
OKUYAMA Tesuro Hokkaido University of Education, Faculty of Education, Asahikawa, Professor, 教育学部・旭川校, 教授 (60128733)
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| Co-Investigator(Kenkyū-buntansha) |
YATSUI Tomoaki Hokkaido University of Education, Faculty of Education, Asahikawa, Assistant Professor, 教育学部・旭川校, 助教授 (00261371)
KOMURO Naoto Hokkaido University of Education, Faculty of Education, Asahikawa, Assistant Professor, 教育学部・旭川校, 助教授 (30195862)
FUKUI Masaki Hokkaido University of Education, Faculty of Education, Asahikawa, Professor, 教育学部・旭川校, 教授 (20002628)
KITAYAMA Masashi Hokkaido University of Education, Faculty of Educauon, Kushiro, Professor, 教育学部・旭川校, 教授 (80169888)
ABE Osamu Hokkaido University of Education, Faculty of Education, Asahikawa, Assistant Professor, 教育学部・旭川校, 助教授 (30202659)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Representations of Finite Groups / Block Algebras / Splendid Tilting Complexes / Broue's Conjecture |
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| Research Abstract |
In the research of this project, we studied Broue's conjecture called "abelian defect conjecture" which is one of main interest in theory of representations of finite groups.
We especially interested in the notion of Splendid tilting complexes intrduced by Rickard and Rouquier. We intended to improve the known method to construct splendid tilting complexes and apply it to solve the conjecture.
1.It has been known that theory of splendid tilting complexes plays well, combining it with theory of relative projective covers. We applied this idea to study finite Chevalley group of small rank. We have already proved the conjecture for the groups Sp(4,q) and in this research we could to prove the conjecture for finite Chevalley group of type G_2.
2.In the above study, the group SU(3,q^2) played some roll. We obtained some sufficient condition that splendid tilting complexes can be lifted to p-central extension. And we could prove that the principal 3-block of SU(3,q^2) is derived equivalent to its Brauer correspondent. We also obtaine similar result for the principal 3-block of the group GU(3,q^2).
3.We also obtained some results concerning cohomology isomorphisms and a splitting of block algebras. We are now sinvestigating the finite Chevalley group of type 2^F_4.
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