Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-05-31
Phys.Atom.Nucl.71:830-835,2008
Physics
High Energy Physics
High Energy Physics - Theory
12 pages. LATEX with revtex4; Proceedings of the XII International Conference on Symmetry Methods in Physics, (Yerevan, 2006)
Scientific paper
10.1134/S1063778808050104
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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