Color Lie rings and PBW deformations of skew group algebras (Q1630098)

The authors study color Lie rings over finite group algebras and the corresponding universal enveloping algebras [\textit{M. Scheunert}, J. Math. Phys. 20, 712--720 (1979; Zbl 0423.17003)]. More precisely, they consider such rings that arise from finite abelian groups acting diagonally on a finite dimensional vector space over a field of characteristic 0 and prove that their universal enveloping algebras can be presented as quantum Drinfeld orbifold algebras [\textit{P. Shroff}, Commun. Algebra 43, No. 4, 1563--1570 (2015; Zbl 1332.16020)]. The proof is mainly based on the theory of PBW deformations and related tools (see, e.g. [\textit{P. Shroff} and \textit{S. Witherspoon}, J. Algebra Appl. 15, No. 3, Article ID 1650049, 15 p. (2016; Zbl 1345.16025)]. As an application they show that these algebras are braided Hopf algebras.