Indecomposable involutive set-theoretical solutions to the Yang-Baxter equation of size $p^2$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913552114122752 |
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| author | Dietzel, Carsten Properzi, Silvia Trappeniers, Senne |
| author_facet | Dietzel, Carsten Properzi, Silvia Trappeniers, Senne |
| contents | The quantum Yang-Baxter equation is a braiding condition on vector spaces which is of high relevance in several fields of mathematics, such as knot theory and quantum group theory. Their combinatorial counterpart are set-theoretic solutions to the Yang--Baxter equation, whose investigation is strongly driven by the study of algebraic objects called (skew) braces. In this article, we focus on indecomposable involutive non-degenerate set-theoretic solutions to the Yang-Baxter equation. More specifically, through a thorough analysis of their associated braces, we give a full classification of those which are of size $p^2$, for $p$ a prime. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_18653 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Indecomposable involutive set-theoretical solutions to the Yang-Baxter equation of size $p^2$ Dietzel, Carsten Properzi, Silvia Trappeniers, Senne Quantum Algebra Group Theory Rings and Algebras 16T25, 20N02, 81R50 The quantum Yang-Baxter equation is a braiding condition on vector spaces which is of high relevance in several fields of mathematics, such as knot theory and quantum group theory. Their combinatorial counterpart are set-theoretic solutions to the Yang--Baxter equation, whose investigation is strongly driven by the study of algebraic objects called (skew) braces. In this article, we focus on indecomposable involutive non-degenerate set-theoretic solutions to the Yang-Baxter equation. More specifically, through a thorough analysis of their associated braces, we give a full classification of those which are of size $p^2$, for $p$ a prime. |
| title | Indecomposable involutive set-theoretical solutions to the Yang-Baxter equation of size $p^2$ |
| topic | Quantum Algebra Group Theory Rings and Algebras 16T25, 20N02, 81R50 |
| url | https://arxiv.org/abs/2403.18653 |