Contractions and deformations of quasi-classical Lie algebras preserving a non-degenerate quadratic Casimir operator
arXiv:0705.4613 · doi:10.1134/S1063778808050104
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.
12 pages. LATEX with revtex4; Proceedings of the XII International Conference on Symmetry Methods in Physics, (Yerevan, 2006) eds. G.S. Pogosyan et al;