Vol. 8, No. 7, 2014

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

Chelsea Walton and Sarah Witherspoon

Vol. 8 (2014), No. 7, 1701–1731
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.

A correction was posted on 3 May 2017 in an online supplement.
Keywords
Hopf algebra, Koszul algebra, PBW deformation, smash product algebra
Mathematical Subject Classification 2010
Primary: 16S80
Secondary: 16E40, 16S37, 16S40