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Contractions and deformations of quasiclassical Lie algebras preserving a nondegenerate quadratic Casimir operator

  • Elementary Particles and Fields
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Abstract

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

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  1. Departamento de Geometria y Topología, Universidad Complutense, Madrid, Spain

    R. Campoamor-Stursberg

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  1. R. Campoamor-Stursberg
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Correspondence to R. Campoamor-Stursberg.

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Campoamor-Stursberg, R. Contractions and deformations of quasiclassical Lie algebras preserving a nondegenerate quadratic Casimir operator. Phys. Atom. Nuclei 71, 830–835 (2008). https://doi.org/10.1134/S1063778808050104

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  • DOI: https://doi.org/10.1134/S1063778808050104

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