Mathematical Research Letters

Volume 25 (2018)

Number 5

Deforming group actions on Koszul algebras

Pages: 1613 – 1644



Anne V. Shepler (Department of Mathematics, University of North Texas, Denton, Tx., U.S.A.)

Sarah Witherspoon (Department of Mathematics, Texas A&M University, College Station, Tx., U.S.A.)


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. Techniques involve a twisted product resolution and the Gerstenhaber bracket on Hochschild cohomology expressed explicitly for cocycles on this resolution.

The first author was partially supported by Simons grant 429539. The second author was partially supported by NSF grant #DMS-1401016.

Received 5 August 2016

Accepted 22 November 2017

Published 1 February 2019