On connection between Rota—Baxter operators and solutions of the classical Yang—Baxter equation with an ad-invariant symmetric part on general linear algebra

M. E. Goncharov

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 81-97

Résumé

In the paper, we find the connection between solutions of the classical Yang—Baxter equation with an ad-invariant symmetric part and Rota—Baxter operators of special type on a real general linear algebra $gl_n(\mathbb R)$. Using this connection, we classify solutions of the classical Yang—Baxter equation with an ad-invariant symmetric part on $gl_2(\mathbb C)$ using the classification of Rota—Baxter operators of nonzero weight on $gl_2(\mathbb C)$ and a classification of Rota—Baxter operators of weight 0 on $sl_2(\mathbb C)$.

Détail

Keywords: Lie bialgebra, Rota—Baxter operator, classical Yang—Baxter equation, general linear Lie algebra.

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