The Yang-Baxter equation and Thompson's group $F$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866912124491530240 |
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| author | Chouraqui, Fabienne |
| author_facet | Chouraqui, Fabienne |
| contents | In analogy with non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation and braces, we define non-degenerate involutive partial set-theoretic solutions and partial braces. We define the structure group and the structure inverse monoid of such a solution and prove that if the partial solution is square-free, then its structure inverse monoid embeds into the restricted product of a commutative inverse monoid and an inverse symmetric monoid. Furthermore, we show that there exists a square-free, non-degenerate involutive partial solution with structure group isomorphic to Thompson's group $F$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_12445 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Yang-Baxter equation and Thompson's group $F$ Chouraqui, Fabienne Group Theory In analogy with non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation and braces, we define non-degenerate involutive partial set-theoretic solutions and partial braces. We define the structure group and the structure inverse monoid of such a solution and prove that if the partial solution is square-free, then its structure inverse monoid embeds into the restricted product of a commutative inverse monoid and an inverse symmetric monoid. Furthermore, we show that there exists a square-free, non-degenerate involutive partial solution with structure group isomorphic to Thompson's group $F$. |
| title | The Yang-Baxter equation and Thompson's group $F$ |
| topic | Group Theory |
| url | https://arxiv.org/abs/2105.12445 |