Hochschild cohomology and Linckelmann cohomology for blocks of finite groups
- Additional Document Info
- View All
Let G be a finite group, F an algebraically closed field of finite characteristic p, and let B be a block of FG. We show that the Hochschild and Linckelmann cohomology rings of B are isomorphic, modulo their radicals, in the cases where (1) B is cyclic and (2) B is arbitrary and G either a nilpotent group or a Frobenius group (p odd). (The second case is a consequence of a more general result.) We give some related results in the more general case that B has a Sylow p-subgroup P as a defect group, giving a precise local description of a quotient of the Hochschild cohomology ring. In case P is elementary abelian, this quotient is isomorphic to the Linckelmann cohomology ring of B, modulo radicals. 2002 Elsevier Science B.V. All rights reserved.
Journal of Pure and Applied Algebra
author list (cited authors)
Pakianathan, J., & Witherspoon, S.
complete list of authors
Pakianathan, Jonathan||Witherspoon, Sarah