Existence of solutions of the classical yang- baxter equation for a real lie Algebra
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We characterize finite-dimensional Lie algebras over the real numbers for which the classical Yang-Baxter equation has a non-trivial skew-symmetric solution (resp. a non-trivial solution with invariant symmetric part). Equivalently, we obtain a characterization of those finite-dimensional real Lie algebras which admit a non-trivial (quasi-) triangular Lie bialgebra structure.
Key words and phrasesClassical Yang-Baxter equation classicalr-matrix (quasi-) triangular Lie bialgebra structure
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