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


  • 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.

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