Structure groupoids of quiver-theoretic Yang-Baxter maps
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908816944136192 |
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| author | Ferri, Davide Shibukawa, Youichi |
| author_facet | Ferri, Davide Shibukawa, Youichi |
| contents | Solutions to the quiver-theoretic quantum Yang-Baxter equation are associated with structure categories and structure groupoids. We prove that the structure groupoids of involutive non-degenerate solutions are Garside. This generalises a well-known result about the structure groups of set-theoretic solutions, due to Chouraqui. We also construct involutive non-degenerate solutions from suitable presented categories. We then investigate the case of solutions of principal homogeneous type. Finally, we present some examples of this new class of Garside groupoids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure groupoids of quiver-theoretic Yang-Baxter maps Ferri, Davide Shibukawa, Youichi Quantum Algebra 16T25, 20L05 Solutions to the quiver-theoretic quantum Yang-Baxter equation are associated with structure categories and structure groupoids. We prove that the structure groupoids of involutive non-degenerate solutions are Garside. This generalises a well-known result about the structure groups of set-theoretic solutions, due to Chouraqui. We also construct involutive non-degenerate solutions from suitable presented categories. We then investigate the case of solutions of principal homogeneous type. Finally, we present some examples of this new class of Garside groupoids. |
| title | Structure groupoids of quiver-theoretic Yang-Baxter maps |
| topic | Quantum Algebra 16T25, 20L05 |
| url | https://arxiv.org/abs/2503.10327 |