On Equivalences between Blocks of Group Algebras: Reduction to the Simple Components
✍ Scribed by Andrei Marcus
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 317 KB
- Volume
- 184
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
A conjecture of Michel Broue states that if D is an abelian Sylow p-subgroup of ´Ž . a finite group G, and H s N D , then the principal blocks of G and H are G Rickard equivalent. The structure of groups with abelian Sylow p-subgroups, as determined by P. Fong and M. E. Harris, raises the following question: Assuming that Broue's conjecture holds for the simple components of G, under what ćonditions does it hold for G itself? Due to the structure of G, this problem
requires mainly the lifting of Rickard complexes to pЈ-extensions of the simple components and the construction of complexes over wreath products. We give here these reduction steps, which may be regarded as a ''Clifford theory'' of tilting complexes.