Algebra & Number Theory

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

Chelsea Walton and Sarah Witherspoon

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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.

Article information

Algebra Number Theory, Volume 8, Number 7 (2014), 1701-1731.

Received: 18 December 2013
Revised: 30 June 2014
Accepted: 29 July 2014
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16S80: Deformations of rings [See also 13D10, 14D15]
Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 16S37: Quadratic and Koszul algebras 16S40: Smash products of general Hopf actions [See also 16T05]

Hopf algebra Koszul algebra PBW deformation smash product algebra


Walton, Chelsea; Witherspoon, Sarah. Poincaré–Birkhoff–Witt deformations of smash product algebras from Hopf actions on Koszul algebras. Algebra Number Theory 8 (2014), no. 7, 1701--1731. doi:10.2140/ant.2014.8.1701.

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