Representations and Cocycle Twists of Color Lie Algebras

By Xiao-Wu Chen, Sergei Silvestrov, F. van Oystaeyen. 2004

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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 ${\text{sl}}^{c}_{2} $.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

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