Dehornoy's class and Sylows for set-theoretical solutions of the Yang-Baxter equation
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913270713024512 |
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| author | Feingesicht, Edouard |
| author_facet | Feingesicht, Edouard |
| contents | We explain how the germ of the structure group of a cycle set decomposes as a product of its Sylow-subgroups, and how this process can be reversed to construct cycle sets from ones with coprime classes. We study Dehornoy's class associated to a cycle set, and conjecture a bound that we prove in a specific case. We combine the use of braces and a monomial representation, in particular to answer a question by Dehornoy on retrieving the Garside structure without a theorem of Rump, while also retrieving said theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02652 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dehornoy's class and Sylows for set-theoretical solutions of the Yang-Baxter equation Feingesicht, Edouard Group Theory We explain how the germ of the structure group of a cycle set decomposes as a product of its Sylow-subgroups, and how this process can be reversed to construct cycle sets from ones with coprime classes. We study Dehornoy's class associated to a cycle set, and conjecture a bound that we prove in a specific case. We combine the use of braces and a monomial representation, in particular to answer a question by Dehornoy on retrieving the Garside structure without a theorem of Rump, while also retrieving said theorem. |
| title | Dehornoy's class and Sylows for set-theoretical solutions of the Yang-Baxter equation |
| topic | Group Theory |
| url | https://arxiv.org/abs/2302.02652 |