Color Lie rings and PBW deformations of skew group algebras

Fryer, S.; Kanstrup, T.; Kirkman, E.; Shepler, A. V.; Witherspoon, S.

doi:10.1016/j.jalgebra.2018.10.012

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Color Lie rings and PBW deformations of skew group algebras

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Kanstrup, T.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.jalgebra.2018.10.012
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Fryer, S., Kanstrup, T., Kirkman, E., Shepler, A. V., & Witherspoon, S. (2019). Color Lie rings and PBW deformations of skew group algebras. Journal of Algebra, 518, 211-236. doi:10.1016/j.jalgebra.2018.10.012.

Cite as: https://hdl.handle.net/21.11116/0000-0004-89D6-0

Abstract

We investigate color Lie rings over finite group algebras and their universal enveloping algebras. We exhibit these universal enveloping algebras as PBW deformations of skew group algebras: Every color Lie ring over a finite group algebra with a particular Yetter-Drinfeld structure has universal enveloping algebra that is a quantum Drinfeld orbifold algebra. Conversely, every quantum Drinfeld orbifold algebra of a particular type arising from the action of an abelian group is the universal enveloping algebra of some color Lie ring over
the group algebra. One consequence is that these quantum Drinfeld orbifold algebras are braided Hopf algebras.