New simple solutions of the Yang--Baxter equation and their permutation groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929377960263680 |
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| author | Cedo, Ferran Okninski, Jan |
| author_facet | Cedo, Ferran Okninski, Jan |
| contents | A new class of indecomposable, irretractable, involutive, non-degenerate set-theoretic solutions of the Yang--Baxter equation is constructed. This class complements the class of such solutions constructed in \cite{CO22} and together they generalize the class of solutions described in \cite[Theorem 4.7{CO21}. Necessary and sufficient conditions are found in order that these new solutions are simple. For a rich subclass of these solutions the structure of their permutation groups, considered as left braces, is determined. In particular, these results answer a question stated in \cite{CO21}. In the finite case, all these solutions have square cardinality. A new class of finite simple solutions of non-square cardinality such that their permutation groups are simple left braces is also constructed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12904 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New simple solutions of the Yang--Baxter equation and their permutation groups Cedo, Ferran Okninski, Jan Quantum Algebra Group Theory 16T25, 20B15, 20F16 A new class of indecomposable, irretractable, involutive, non-degenerate set-theoretic solutions of the Yang--Baxter equation is constructed. This class complements the class of such solutions constructed in \cite{CO22} and together they generalize the class of solutions described in \cite[Theorem 4.7{CO21}. Necessary and sufficient conditions are found in order that these new solutions are simple. For a rich subclass of these solutions the structure of their permutation groups, considered as left braces, is determined. In particular, these results answer a question stated in \cite{CO21}. In the finite case, all these solutions have square cardinality. A new class of finite simple solutions of non-square cardinality such that their permutation groups are simple left braces is also constructed. |
| title | New simple solutions of the Yang--Baxter equation and their permutation groups |
| topic | Quantum Algebra Group Theory 16T25, 20B15, 20F16 |
| url | https://arxiv.org/abs/2401.12904 |