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

Chelsea Walton; Sarah Witherspoon

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 Sarah Witherspoon

Year: 2014 Journal: Algebra & Number Theory Vol: 8 (7)Pages: 1701-1731 Publisher: Mathematical Sciences Publishers

DOI: 10.2140/ant.2014.8.1701

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Abstract

Let [math] be a Hopf algebra and let [math] be a Koszul [math] -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 [math] . Many examples of these deformations are given.

Keywords:

Hopf algebra Mathematics Algebra over a field Product (mathematics) Pure mathematics Poincaré conjecture Filtered algebra Geometry

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Algebraic structures and combinatorial models

Physical Sciences → Mathematics → Geometry and Topology

Advanced Topics in Algebra

Physical Sciences → Mathematics → Algebra and Number Theory

Nonlinear Waves and Solitons

Physical Sciences → Physics and Astronomy → Statistical and Nonlinear Physics

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

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