This article is cited in 3 papers

Mathematical logic, algebra and number theory

On Rota–Baxter operators of non-zero weight arisen from the solutions of the classical Yang–Baxter equation

M. E. Goncharov<sup>ab

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

Abstract: Let $L$ be a simple anti-commutative algebra. In this paper we prove that a non skew-symmetric solution of the classical Yang–Baxter equation on $L$ with $L$-invariant symmetric part induces on $L$ a Rota–Baxter operator of a non-zero weight.

Keywords: Rota–Baxter operator, anti-commutative algebra, Lie algebra, Malcev algebra, non-associative bialgebra, classical Yang–Baxter equation.

UDC: 512.554

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

Received October 27, 2017, published December 29, 2017

Language: English

DOI: 10.17377/semi.2017.14.132

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