Retracts of degenerate solutions of the Yang-Baxter equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909752250859520 |
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| author | Jedlička, Přemysl Pilitowska, Agata |
| author_facet | Jedlička, Přemysl Pilitowska, Agata |
| contents | Most of the set-theoretical solutions of the Yang-Baxter equation studied in the past years were non-degenerate multipermutation solutions. For degenerate solutions, a correct definition of multipermutation solutions has not been established so far. We fill here this gap providing a definition of multipermutation solutions that generalizes the one for non-degenerate solutions and we find an axiomatic description of this class by a set of equations that generalizes the equations describing non-degenerate multipermutation solutions.
It turned out that the results do not need all the properties of solutions of the Yang-Baxter equation and therefore we prove them in a general universal-algebraic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17987 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Retracts of degenerate solutions of the Yang-Baxter equation Jedlička, Přemysl Pilitowska, Agata Mathematical Physics Primary: 16T25. Secondary: 06B10, 08A30 Most of the set-theoretical solutions of the Yang-Baxter equation studied in the past years were non-degenerate multipermutation solutions. For degenerate solutions, a correct definition of multipermutation solutions has not been established so far. We fill here this gap providing a definition of multipermutation solutions that generalizes the one for non-degenerate solutions and we find an axiomatic description of this class by a set of equations that generalizes the equations describing non-degenerate multipermutation solutions. It turned out that the results do not need all the properties of solutions of the Yang-Baxter equation and therefore we prove them in a general universal-algebraic setting. |
| title | Retracts of degenerate solutions of the Yang-Baxter equation |
| topic | Mathematical Physics Primary: 16T25. Secondary: 06B10, 08A30 |
| url | https://arxiv.org/abs/2508.17987 |