Poincare-Birkhoff-Witt deformations of smash product algebras from Hopf actions on Koszul algebras

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 Poincare-Birkhoff-Witt (PBW) deformation of the smash product algebra B#H. Many examples of these deformations are given.

v4: The hypothesis that dim(V) \geq 3 in main result has been removed as it was not needed

References in corpus (2)

• Infinitesimal Cherednik algebras as W-algebras
• Infinitesimal Hecke algebras of so_N

Cited by in corpus (7)

• Resolutions for Twisted Tensor Products
• Poincare-Birkhoff-Witt Theorems
• Generalized nil-Coxeter algebras, cocommutative algebras, and the PBW property
• Weyl algebras for quantum homogeneous spaces
• $PBW$-deformations of graded rings
• PBW-deformations of smash products involving Hopf algebra of Kac-Paljutkin type
• PBW deformations of Koszul algebras over a nonsemisimple ring