Representations and Cocycle Twists of Color Lie Algebras

Xiao-Wu Chen; Sergei D. Silvestrov; Fred van Oystaeyen

paper

Representations and Cocycle Twists of Color Lie Algebras

arXiv:math/0407165

Abstract

We study relations between finite-dimensional representations of color Lie algebras and their cocycle twists. Main tools are the universal enveloping algebras and their FCR-properties (finite-dimensional representations are completely reducible.) Cocycle twist preserves the FCR-property. As an application, we compute all finite dimensional representations (up to isomorphism) of the color Lie algebra $s l_{2}^{c}$ .

18 pages, with an concrete example