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

Ballester-Bolinches, A. ; Esteban-Romero, R. ; Jiménez-Seral, P. (Universidad de Zaragoza) ; Pérez-Calabuig, V.

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.aim.2024.109880

Año: 2024

Publicado en: Advances in Mathematics 455 (2024), 109880 [27 pp.]
ISSN: 0001-8708

Tipo y forma: Article (Published version)

Área (Departamento): Área Algebra (Dpto. Matemáticas)