On dynamical skew braces and skew bracoids
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915294324195328 |
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| author | Ferri, Davide |
| author_facet | Ferri, Davide |
| contents | Dynamical skew braces are known to produce solutions to the quiver-theoretic Yang--Baxter equation. Under a technical hypothesis, we prove that these solutions are braided groupoids (and hence skew bracoids in the sense of Sheng, Tang and Zhu). Conversely, every connected braided groupoid can be parallelised, making it isomorphic to a dynamical skew brace. We study the combinatorics of these objects, depending on some strings of integer invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On dynamical skew braces and skew bracoids Ferri, Davide Quantum Algebra Group Theory 16T25, 81R50 Dynamical skew braces are known to produce solutions to the quiver-theoretic Yang--Baxter equation. Under a technical hypothesis, we prove that these solutions are braided groupoids (and hence skew bracoids in the sense of Sheng, Tang and Zhu). Conversely, every connected braided groupoid can be parallelised, making it isomorphic to a dynamical skew brace. We study the combinatorics of these objects, depending on some strings of integer invariants. |
| title | On dynamical skew braces and skew bracoids |
| topic | Quantum Algebra Group Theory 16T25, 81R50 |
| url | https://arxiv.org/abs/2410.10717 |