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

TL;DR

This paper demonstrates that non skew-symmetric solutions to the classical Yang-Baxter equation on simple anti-commutative algebras induce Rota-Baxter operators of non-zero weight, revealing a new link between these algebraic structures.

Contribution

It establishes a novel connection between solutions of the classical Yang-Baxter equation and Rota-Baxter operators on simple anti-commutative algebras.

Findings

Non skew-symmetric solutions induce Rota-Baxter operators of non-zero weight.

The result applies specifically to simple anti-commutative algebras.

Provides a new method to construct Rota-Baxter operators from Yang-Baxter solutions.

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.