Project/Area Number  10640001 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Algebra

Research Institution  Hokkaido University of Education 
Principal Investigator 
OKUYAMA Tetsuro Hokkaido University of Education, Faculty of Education, Asahikawa, Professor, 教育学部・旭川校, 教授 (60128733)

CoInvestigator(Kenkyūbuntansha) 
浅芝 秀人 大阪市立大学, 理学部, 助教授 (70175165)
NISHIMURA Junichi Faculty of Education, Sapporo., Assistant Professor, 教育学部・札幌校, 助教授 (00025488)
ABE Osamu Faculty of Education, Asahikawa., Assistant Professor, 教育学部・旭川校, 助教授 (30202659)
YATSUI Tomoaki Faculty of Education, Asahikawa., Assistant Professor, 教育学部・旭川校, 助教授 (00261371)
FUKUI Masaki Faculty of Education, Asahikawa., Professor, 教育学部・旭川校, 教授 (20002628)
KITAYAMA Masashi Faculty of Education, Kushiro., Assistant Professor, 教育学部・釧路校, 助教授 (80169888)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥3,200,000 (Direct Cost : ¥3,200,000)
Fiscal Year 1999 : ¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1998 : ¥1,800,000 (Direct Cost : ¥1,800,000)

Keywords  FINITE GROUPS / MODULAR REPRESENTATION / BLOCK THEORY / BROUES CONJECTURE / DERIVED EQUIVALENCES / 有限群 / モジュラー表現 / ブロック理論 / ブルエ予想 / 導来同値 
Research Abstract 
In the research of this project, we studied a conjecture by Broue which says that a block algebra with abelian defect group of a finite group is derived equivalent to its Brauer correspondent. And we obtained good results as follows : 1. We could give some methods to construct tilting complexes for two symmetric algebras which are stably equivalent of Morita type. As applications of our methods, we could show that the conjectures are true for principal 3blocks of some finite groups with elementary abelian Sylow 3subgroup of order 9, for example, Matieu groups M11, M21(=SL(3,4)), M22,M23 and HignanSims group HS. We could also checked the conjecture for the principal blocks of the groups SL(2,q) over defining characteristic. 2. There are many examples of blocks which are not known to be stably equivalent to its Brauer correspondent. We studied the principal 2block of the smallest group of Janko. Using the splendid tilting complex for SL(2,4) given by Rickard , we could show that the conjecture is true for this block. We could also decide unknown parameters in the decomposition numbers of the group U(3,q) . We believe that our result can be used to study the conjecture for this group. 3. Related to Broue's conjecture, there have been studied on tensor decompositions of blocks as algebras. We obtained some result on this problem by making use of theory of separable algebras and Puigis theory of source algebras of blocks.
