Poincare-Birkhoff-Witt deformations of smash product algebras from Hopf actions on Koszul algebras

TL;DR

This paper characterizes when certain algebra deformations, arising from Hopf algebra actions on Koszul algebras, satisfy the PBW property, providing conditions and examples for these deformations.

Contribution

It establishes necessary and sufficient conditions for PBW deformations of smash product algebras from Hopf actions on Koszul algebras, with numerous examples.

Findings

Derived explicit criteria for PBW deformations

Provided multiple concrete examples of such deformations

Extended understanding of algebraic structures under Hopf actions

Abstract

Let H be a Hopf algebra and let B be a Koszul H-module algebra. We provide necessary and sufficient conditions for a filtered algebra to be a Poincare-Birkhoff-Witt (PBW) deformation of the smash product algebra B#H. Many examples of these deformations are given.