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arXiv · 2304.13475

Soluble skew left braces and soluble solutions of the Yang-Baxter equation

Adolfo Ballester-Bolinches·Ramón Esteban-Romero·Paz Jiménez-Seral·Vicent Pérez-Calabuig
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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.

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Adolfo Ballester-Bolinches, Ramón Esteban-Romero, Paz Jiménez-Seral, Vicent Pérez-Calabuig. 2023-04-26. Soluble skew left braces and soluble solutions of the Yang-Baxter equation. https://arxiv.org/abs/2304.13475

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