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

Walton, Chelsea; Witherspoon, Sarah

doi:10.2140/ant.2014.8.1701

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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

DOI: 10.2140/ant.2014.8.1701

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

Milestones

Received: 18 December 2013

Revised: 30 June 2014

Accepted: 29 July 2014

Published: 21 October 2014

Corrected: 3 May 2017

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

Vol. 8, No. 7, 2014