Color Lie rings and PBW deformations of skew group algebras

JOURNAL OF ALGEBRA

卷:518

Article

Fryer, S.¹  Kanstrup, T.²  Kirkman, E.³  Shepler, A. V.⁴  Witherspoon, S.⁵ 

[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

[2] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

[3] Wake Forest Univ, Dept Math, POB 7388, Winston Salem, NC 27109 USA

[4] Univ North Texas, Dept Math, Denton, TX 76203 USA

[5] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

关键词: Color Lie algebras;    Skew group algebras;    Deformation theory;    Hopf algebras;    Drinfeld Hecke algebras;    Rational Cherednik algebras;   

DOI  :  10.1016/j.jalgebra.2018.10.012

来源: Elsevier

【 摘 要 】

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 a 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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