Representations and Cocycle Twists of Color Lie Algebras

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

Representations and Cocycle Twists of Color Lie Algebras

Representation Theory 2007-05-23 v5 Rings and Algebras

Authors: Xiao-Wu Chen , Sergei D. Silvestrov , Fred van Oystaeyen

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 $sl_2^c$ .

Keywords

color lie algebras representations cocycle twists universal enveloping algebras fcr-property

Cite

@article{arxiv.math/0407165,
  title  = {Representations and Cocycle Twists of Color Lie Algebras},
  author = {Xiao-Wu Chen and Sergei D. Silvestrov and Fred van Oystaeyen},
  journal= {arXiv preprint arXiv:math/0407165},
  year   = {2007}
}

Comments

18 pages, with an concrete example

Representations and Cocycle Twists of Color Lie Algebras

Abstract

Keywords

Cite

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