Affiliation:
1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
Abstract
Given a skew left brace [Formula: see text], a method is given to construct all the non-degenerate set-theoretic solutions [Formula: see text] of the Yang–Baxter equation such that the associated permutation group [Formula: see text] is isomorphic, as a skew left brace, to [Formula: see text]. This method depends entirely on the brace structure of [Formula: see text]. We then adapt this method to show how to construct solutions with additional properties, like square-free, involutive or irretractable solutions. Using this result, it is even possible to recover racks from their permutation group.
Funder
Secretaría de Estado de Investigación, Desarrollo e Innovación
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
28 articles.
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1. Skew left braces and 2-reductive solutions of the Yang-Baxter equation;Journal of Pure and Applied Algebra;2024-04
2. On two-sided skew braces;Journal of Algebra;2023-10
3. Isoclinism of skew braces;Bulletin of the London Mathematical Society;2023-08-04
4. New Structure of Skew Braces and Their Ideals;IOCMA 2023;2023-05-15
5. On bi-skew braces and brace blocks;Journal of Pure and Applied Algebra;2023-05