The Hochschild Cohomology Ring of a Group Algebra

Abstract

There is a standard additive decomposition of the Hochschild cohomology ring of the group algebra of a finite group G as the direct sum of the cohomology rings of the centralizers of representatives of the conjugacy classes of G. A special case of our main result describes the cup product in terms of this decomposition. As applications, we determine presentations for the Hochschild cohomology rings of [(1)] the mod-3 group algebra of the symmetric group S3, [(2)] the mod-2 group algebra of the alternating group A4, and [(3)] the mod-2 group algebras of the dihedral 2-groups. 1991 Mathematics Subject Classification: 16E40, 20J06.