On Rota-Baxter operators of non-zero weight induced by non skew-symmetric solutions of the classical Yang-baxter equation on simple anticommutative algebras

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.