This article is cited in 6 papers

Mathematical logic, algebra and number theory

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

M. E. Goncharov<sup>ab

a</sup> Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
^b Department of Mechanics and Mathematics, Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia

Abstract: 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.

UDC: 512.554

MSC: 16T25,17B62,17D10,17A36

Received September 30, 2019, published December 27, 2019

Language: English

DOI: 10.33048/semi.2019.16.149

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