Rota-Baxter groups, skew left braces, and the Yang-Baxter equation
Abstract
Braces were introduced by W. Rump in 2006 as an algebraic system related to the quantum Yang-Baxter equation. In 2017, L. Guarnieri and L. Vendramin defined for the same purposes a more general notion of a skew left brace. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] gave a definition of what is a Rota-Baxter operator on a group. We connect these two notions as follows. It is shown that every Rota-Baxter group gives rise to a skew left brace. Moreover, every skew left brace can be injectively embedded into a Rota-Baxter group. When the additive group of a skew left brace is complete, then this brace is induced by a Rota-Baxter group. We interpret some notions of the theory of skew left braces in terms of Rota-Baxter operators.
Keywords
Cite
@article{arxiv.2105.00428,
title = {Rota-Baxter groups, skew left braces, and the Yang-Baxter equation},
author = {Valeriy G. Bardakov and Vsevolod Gubarev},
journal= {arXiv preprint arXiv:2105.00428},
year = {2022}
}
Comments
25 p.; v2: section 5.2 is rewritten (after remarks of I. Colazzo and L. Vendramin)