Generalized Lie Algebras and Cocycle Twists |
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Authors: | Mikhail Kochetov |
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Institution: | 1. Department of Mathematics and Statistics , Memorial University of Newfoundland , St. John's, Newfoundland, Canada mikhail@math.mun.ca |
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Abstract: | We use the results of Etingof and Gelaki on the classification of (co)triangular Hopf algebras to extend Scheunert's “discoloration” technique to Lie algebras in the category of (co)modules. As an application, we prove a PBW-type theorem for such Lie algebras. We also discuss the relationship between Lie algebras in the category of (co)modules and symmetric braided Lie algebras introduced by Gurevich. Finally, we construct examples of symmetric braided Lie algebras that are essentially different from Lie coloralgebras. |
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Keywords: | Braiding Cocycle Coloralgebra Hopf algebra Lie algebra Superalgebra |
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