Deforming group actions on Koszul algebras

TL;DR

This paper establishes conditions for PBW deformations of skew group algebras arising from finite groups acting on Koszul algebras, including cases where the characteristic divides the group order, affecting both group actions and relations.

Contribution

It provides Braverman-Gaitsgory style criteria for deformations of skew group algebras in a broad setting, encompassing characteristic dividing scenarios.

Findings

Derived explicit deformation conditions for skew group algebras

Extended deformation theory to cases with characteristic dividing group order

Unified treatment of group action and relation deformations

Abstract

We give Braverman-Gaitsgory style conditions for general PBW deformations of skew group algebras formed from finite groups acting on Koszul algebras. When the characteristic divides the order of the group, this includes deformations of the group action as well as of the Koszul relations.