One-generator skew braces and indecomposable set-theoretic solutions to the Yang-Baxter equation
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912429919698944 |
|---|---|
| author | Castelli, Marco |
| author_facet | Castelli, Marco |
| contents | We study the class of one-generator solutions to the Yang-Baxter equation, extending some recent results concerning the classes of involutive and multipermutation solutions. Moreover we show the precise relationship between indecomposable solutions to the Yang-Baxter equation and finite one-generator skew braces, giving a positive answer to a question posed by Agata and Alicja Smoktunowicz. In the last part, we apply our results to the involutive case, and we present some numerical results involving solutions of small size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One-generator skew braces and indecomposable set-theoretic solutions to the Yang-Baxter equation Castelli, Marco Quantum Algebra We study the class of one-generator solutions to the Yang-Baxter equation, extending some recent results concerning the classes of involutive and multipermutation solutions. Moreover we show the precise relationship between indecomposable solutions to the Yang-Baxter equation and finite one-generator skew braces, giving a positive answer to a question posed by Agata and Alicja Smoktunowicz. In the last part, we apply our results to the involutive case, and we present some numerical results involving solutions of small size. |
| title | One-generator skew braces and indecomposable set-theoretic solutions to the Yang-Baxter equation |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2506.12503 |