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arXiv · 0705.4613

Contractions and deformations of quasi-classical Lie algebras preserving a non-degenerate quadratic Casimir operator

R. Campoamor-Stursberg
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Abstract

By means of contractions of Lie algebras, we obtain new classes of indecomposable quasi-classical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise naturally from non-compact real simple algebras with non-simple complexification, where we impose that a non-degenerate quadratic Casimir operator is preserved by the limiting process. We further consider the converse problem, and obtain sufficient conditions on integrable cocycles of quasi-classical Lie algebras in order to preserve non-degenerate quadratic Casimir operators by the associated linear deformations.

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R. Campoamor-Stursberg. 2007-05-31. Contractions and deformations of quasi-classical Lie algebras preserving a non-degenerate quadratic Casimir operator. https://doi.org/10.1134/s1063778808050104

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