Rota-Baxter operators and non-skew-symmetric solutions of the classical Yang-Baxter equation on quadratic Lie algebras


Abstract in English

We study possible connections between Rota-Baxter operators of non-zero weight and non-skew-symmetric solutions of the classical Yang-Baxter equation on finite-dimensional quadratic Lie algebras. The particular attention is made to the case when for a solution $r$ the element $r+tau(r)$ is $L$-invariant.

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