Solutions of the Yang-Baxter equation and strong semilattices of skew braces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917618686885888 |
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| author | Catino, Francesco Mazzotta, Marzia Stefanelli, Paola |
| author_facet | Catino, Francesco Mazzotta, Marzia Stefanelli, Paola |
| contents | We prove that any set-theoretic solution of the Yang-Baxter equation associated to a dual weak brace is a strong semilattice of non-degenerate bijective solutions. This fact makes use of the description of any dual weak brace $S$ we provide in terms of strong semilattice $Y$ of skew braces $B_α$, with $α\in Y$. Additionally, we describe the ideals of $S$ and study its nilpotency by correlating it to that of each skew brace $B_α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03540 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solutions of the Yang-Baxter equation and strong semilattices of skew braces Catino, Francesco Mazzotta, Marzia Stefanelli, Paola Quantum Algebra We prove that any set-theoretic solution of the Yang-Baxter equation associated to a dual weak brace is a strong semilattice of non-degenerate bijective solutions. This fact makes use of the description of any dual weak brace $S$ we provide in terms of strong semilattice $Y$ of skew braces $B_α$, with $α\in Y$. Additionally, we describe the ideals of $S$ and study its nilpotency by correlating it to that of each skew brace $B_α$. |
| title | Solutions of the Yang-Baxter equation and strong semilattices of skew braces |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2307.03540 |