Equivariant one-parameter deformations of associative algebras

TL;DR

This paper develops an equivariant Hochschild cohomology framework to analyze how associative algebras with finite group actions can be deformed while respecting symmetry.

Contribution

It introduces an equivariant deformation cohomology theory for associative algebras with finite group actions, extending classical Hochschild cohomology.

Findings

Defines equivariant Hochschild cohomology for finite group actions

Provides tools to classify equivariant algebra deformations

Lays groundwork for future studies on symmetry-preserving deformations

Abstract

We introduce an equivariant version of Hochschild cohomology as the deformation cohomology to study equivariant deformations of associative algebras equipped with finite group actions.