Simple solutions of the Yang-Baxter equation of cardinality $p^n$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910522532691968 |
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| author | Cedo, Ferran Okninski, Jan |
| author_facet | Cedo, Ferran Okninski, Jan |
| contents | For every prime number p and integer $n>1$, a simple, involutive, non-degenerate set-theoretic solution $(X,r$) of the Yang-Baxter equation of cardinality $|X| = p^n$ is constructed. Furthermore, for every non-(square-free) positive integer m which is not the square of a prime number, a non-simple, indecomposable, irretractable, involutive, non-degenerate set-theoretic solution $(X,r)$ of the Yang-Baxter equation of cardinality $|X| = m$ is constructed. A recent question of Castelli on the existence of singular solutions of certain type is also answered affirmatively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07907 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple solutions of the Yang-Baxter equation of cardinality $p^n$ Cedo, Ferran Okninski, Jan Quantum Algebra 16T25, 20B15, 20F16 For every prime number p and integer $n>1$, a simple, involutive, non-degenerate set-theoretic solution $(X,r$) of the Yang-Baxter equation of cardinality $|X| = p^n$ is constructed. Furthermore, for every non-(square-free) positive integer m which is not the square of a prime number, a non-simple, indecomposable, irretractable, involutive, non-degenerate set-theoretic solution $(X,r)$ of the Yang-Baxter equation of cardinality $|X| = m$ is constructed. A recent question of Castelli on the existence of singular solutions of certain type is also answered affirmatively. |
| title | Simple solutions of the Yang-Baxter equation of cardinality $p^n$ |
| topic | Quantum Algebra 16T25, 20B15, 20F16 |
| url | https://arxiv.org/abs/2407.07907 |