Vol. 8, No. 7, 2014

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ISSN: 1944-7833 (e-only)
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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.

Keywords
Hopf algebra, Koszul algebra, PBW deformation, smash product algebra
Mathematical Subject Classification 2010
Primary: 16S80
Secondary: 16E40, 16S37, 16S40
Milestones
Received: 18 December 2013
Revised: 30 June 2014
Accepted: 29 July 2014
Published: 21 October 2014
Authors
Chelsea Walton
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139
United States
Sarah Witherspoon
Department of Mathematics
Texas A&M University
College Station, TX 77843
United States