Soluble skew left braces and soluble solutions of the Yang-Baxter equation
Group Theory
2024-08-15 v3 Rings and Algebras
Abstract
The study of non-degenerate set-theoretic solutions of the Yang-Baxter equation calls for a deep understanding of the algebraic structure of a skew left brace. In this paper, the skew brace theoretical property of solubility is introduced and studied. It leads naturally to the notion of solubility of solutions of the Yang-Baxter equation. It turns out that soluble non-degenerate set-theoretic solutions are characterised by soluble skew left braces. The rich ideal structure of soluble skew left braces is also shown. A worked example showing the relevance of the brace theoretical property of solubility is also presented.
Cite
@article{arxiv.2304.13475,
title = {Soluble skew left braces and soluble solutions of the Yang-Baxter equation},
author = {Adolfo Ballester-Bolinches and Ramón Esteban-Romero and Paz Jiménez-Seral and Vicent Pérez-Calabuig},
journal= {arXiv preprint arXiv:2304.13475},
year = {2024}
}
Comments
31 pages; minor changes have been introduced; accepted to be published in Advances in Mathematics