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THE HOCHSCHILD COHOMOLOGY RING OF A GROUP ALGEBRA

Published online by Cambridge University Press:  01 July 1999

STEPHEN F. SIEGEL  and
SARAH J. WITHERSPOON
STEPHEN F. SIEGEL
Affiliation:
Department of Computer Science, University of Massachusetts, Amherst, MA 01003-4515, U.S.A. E-mail:[email protected]
SARAH J. WITHERSPOON
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, U.S.A. E-mail:[email protected]
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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 $S_3$,

[(2)] the mod-$2$ group algebra of the alternating group $A_4$, and

[(3)] the mod-$2$ group algebras of the dihedral $2$-groups.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 79 , Issue 1 , July 1999 , pp. 131 - 157
Copyright
London Mathematical Society 1999

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