Hochschild cohomology and Linckelmann cohomology for blocks of finite groups Academic Article

abstract

• 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.

authors

• Witherspoon, Sarah

published proceedings

• Journal of Pure and Applied Algebra

author list (cited authors)

• Pakianathan, J., & Witherspoon, S.

citation count

• 2

complete list of authors

• Pakianathan, Jonathan||Witherspoon, Sarah

publication date

• January 2003

publisher

• Elsevier  Publisher

published in

• Journal of Pure and Applied Algebra  Journal

Digital Object Identifier (DOI)

• 10.1016/s0022-4049(02)00189-5

start page

• 87

end page

• 100

volume

• 178

issue

• 1

URL

• http://dx.doi.org/10.1016/s0022-4049(02)00189-5