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.