Geodesic
On connection between Rota---Baxter operators and solutions of the classical Yang---Baxter equation with an ad-invariant symmetric part on general linear algebra
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 81-97.

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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 $sl_2(\mathbb C)$.
Keywords: Lie bialgebra, Rota—Baxter operator, classical Yang—Baxter equation, general linear Lie algebra. 
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     title = {On connection between {Rota---Baxter} operators and solutions of the classical {Yang---Baxter} equation with an ad-invariant symmetric part on general linear algebra},
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M. E. Goncharov. On connection between Rota---Baxter operators and solutions of the classical Yang---Baxter equation with an ad-invariant symmetric part on general linear algebra. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 81-97. http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a3/