Non-involutive solutions of the Yang-Baxter equation of multipermutation level 2
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914852893622272 |
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| author | Hora, Jan Jedlicka, Premysl Pilitowska, Agata |
| author_facet | Hora, Jan Jedlicka, Premysl Pilitowska, Agata |
| contents | We study non-degenerate set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2 which are not 2-reductive. We describe an effective way of constructing such solutions using square-free 2-reductive solutions and two bijections. We present an algorithm how to obtain all such finite solutions, up to isomorphism. Using this algorithm, we enumerate all solutions of multipermutation level 2 up to size 6. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_00755 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-involutive solutions of the Yang-Baxter equation of multipermutation level 2 Hora, Jan Jedlicka, Premysl Pilitowska, Agata Rings and Algebras Primary: 16T25 Secondary: 20N05, 20B25 We study non-degenerate set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2 which are not 2-reductive. We describe an effective way of constructing such solutions using square-free 2-reductive solutions and two bijections. We present an algorithm how to obtain all such finite solutions, up to isomorphism. Using this algorithm, we enumerate all solutions of multipermutation level 2 up to size 6. |
| title | Non-involutive solutions of the Yang-Baxter equation of multipermutation level 2 |
| topic | Rings and Algebras Primary: 16T25 Secondary: 20N05, 20B25 |
| url | https://arxiv.org/abs/2407.00755 |