The Lie structure on the Hochschild cohomology of a modular group algebra

TL;DR

This paper demonstrates that the Gerstenhaber bracket on Hochschild cohomology of a cyclic group algebra over a field of positive characteristic is non-trivial and relates it to a Witt-type algebra.

Contribution

It establishes the non-triviality of the Gerstenhaber bracket and connects the Lie algebra structure to Witt-type algebras in positive characteristic.

Findings

Gerstenhaber bracket is non-trivial for cyclic group algebra

Lie algebra structure relates to Witt-type algebra

Provides new insights into Hochschild cohomology in positive characteristic

Abstract

We prove that the Gerstenhaber bracket on the Hochschild cohomology of the group algebra of a cyclic group over a field of positive characteristic is not trivial. In this case, we relate the Lie algebra structure on the odd degrees of the Hochschild cohomology with a Witt-type algebra.