Soluble skew left braces and soluble solutions of the Yang-Baxter equation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2023
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| author | Ballester-Bolinches, Adolfo Esteban-Romero, Ramón Jiménez-Seral, Paz Pérez-Calabuig, Vicent |
| author_facet | Ballester-Bolinches, Adolfo Esteban-Romero, Ramón Jiménez-Seral, Paz Pérez-Calabuig, Vicent |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13475 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Soluble skew left braces and soluble solutions of the Yang-Baxter equation Ballester-Bolinches, Adolfo Esteban-Romero, Ramón Jiménez-Seral, Paz Pérez-Calabuig, Vicent Group Theory Rings and Algebras 16T25, 16N40, 81R50 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. |
| title | Soluble skew left braces and soluble solutions of the Yang-Baxter equation |
| topic | Group Theory Rings and Algebras 16T25, 16N40, 81R50 |
| url | https://arxiv.org/abs/2304.13475 |