Geodesic
Rota-Baxter operators and non-skew-symmetric solutions of the classical Yang--Baxter equation on quadratic Lie algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 2098-2109

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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.
Keywords: Rota–Baxter operator, quadratic Lie algebra, non-associative bialgebra, classical Yang–Baxter equation. 
@article{SEMR_2019_16_a35,
     author = {M. E. Goncharov},
     title = {Rota-Baxter operators and non-skew-symmetric solutions of the classical {Yang--Baxter} equation on quadratic {Lie} algebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {2098--2109},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a35/}
}
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M. E. Goncharov. Rota-Baxter operators and non-skew-symmetric solutions of the classical Yang--Baxter equation on quadratic Lie algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 2098-2109. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a35/