تقرير
Soluble skew left braces and soluble solutions of the Yang-Baxter equation
| العنوان: | Soluble skew left braces and soluble solutions of the Yang-Baxter equation |
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| المؤلفون: | Ballester-Bolinches, Adolfo, Esteban-Romero, Ramón, Jiménez-Seral, Paz, Pérez-Calabuig, Vicent |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - Rings and Algebras, 16T25, 16N40, 81R50 |
| الوصف: | 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. Comment: 31 pages; minor changes have been introduced; accepted to be published in Advances in Mathematics |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2304.13475 |
| رقم الأكسشن: | edsarx.2304.13475 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |