The Gerstenhaber bracket as a Schouten bracket for polynomial rings extended by finite groups

TL;DR

This paper demonstrates that Gerstenhaber brackets on Hochschild cohomology of skew group algebras formed from polynomial rings and finite groups can be expressed using Schouten brackets, providing new insights and conditions for when brackets vanish.

Contribution

It introduces a novel technique to relate Gerstenhaber brackets to Schouten brackets in the context of polynomial rings extended by finite groups.

Findings

Gerstenhaber brackets can be expressed as Schouten brackets in this setting

Conditions are identified under which the brackets are always zero

Strengthens existing results on Hochschild cohomology of skew group algebras

Abstract

We apply new techniques to Gerstenhaber brackets on the Hochschild cohomology of a skew group algebra formed from a polynomial ring and a finite group (in characteristic 0). We show that the Gerstenhaber brackets can always be expressed in terms of Schouten brackets. We obtain as consequences some conditions under which brackets are always 0, strengthening known results.