Computations of the Hochschild Cohomology of Group Algebras

TL;DR

This paper advances the computation of Hochschild cohomology rings of group algebras, extending previous results and providing explicit calculations for groups of order less than 16 and specific semidirect products.

Contribution

It applies the product formula to compute Hochschild cohomology for small group algebras and offers an alternative approach for certain semidirect product cases.

Findings

Computed Hochschild cohomology algebra for groups with order less than 16.

Provided an alternative computation for the ring HH^*(k(E imes P)).

Extended existing computations using the product formula.

Abstract

The Hochschild cohomology ring of a group algebra is an object that has received recent attention, but is difficult to compute, in even the simplest of cases. In this paper, we use the product formula due to Witherspoon and Siegel to extend some of their computations. In particular, we compute the Hochschild cohomology algebra of group algebras kG where |G| is less than 16, and we provide an alternative computation of the ring $HH^*(k(E \ltimes P))$ considered by Kessar and Linckelmann.