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arXiv:2304.13475 [math.GR]AbstractReferencesReviewsResources

On solubility of skew left braces and solutions of the Yang-Baxter equation

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

Published 2023-04-26Version 1

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, we describe finite skew left braces admitting no proper substructure, we introduce a suitable notion of solubility of skew left braces and study the ideal structure of soluble skew left braces. As a consequence, results on decomposability of solutions are also obtained.

Comments: 18 pages
Categories: math.GR, math.RA
Subjects: 16T25, 16N40, 81R50
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