Soluble skew left braces and soluble solutions of the Yang-Baxter equation
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2023
- DOI:
- 10.48550/arXiv.2304.13475
- arXiv:
- arXiv:2304.13475
- Bibcode:
- 2023arXiv230413475B
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Rings and Algebras;
- 16T25;
- 16N40;
- 81R50
- E-Print:
- 31 pages