Poincaré–Birkhoff–Witt deformations of smash product algebras from Hopf actions on Koszul algebras

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 Poincaré–Birkhoff–Witt (PBW) deformation of the smash product algebra $B\#H$. Many examples of these deformations are given.