Quasi racks, quasi bijective and quasi non-degenerate set-theoretic solutions of the Yang-Baxter equation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909956948623360 |
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| author | Mazzotta, Marzia Stefanelli, Paola Wiertel, Magdalena |
| author_facet | Mazzotta, Marzia Stefanelli, Paola Wiertel, Magdalena |
| contents | This work initiates a systematic study of the class of quasi bijective and quasi non-degenerate solutions to the set-theoretic Yang-Baxter equation. The motivation stems from the observation that solutions that arise from dual weak braces belong to these classes. The notions of quasi rack and derived solution are introduced and examined, extending the classical definitions. Additionally, a family of quasi left non-degenerate solutions is described in terms of quasi racks and g-twists, analogous to the left non-degenerate case. Furthermore, we completely characterize a class of quasi racks that are Plonka sum of racks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi racks, quasi bijective and quasi non-degenerate set-theoretic solutions of the Yang-Baxter equation Mazzotta, Marzia Stefanelli, Paola Wiertel, Magdalena Quantum Algebra This work initiates a systematic study of the class of quasi bijective and quasi non-degenerate solutions to the set-theoretic Yang-Baxter equation. The motivation stems from the observation that solutions that arise from dual weak braces belong to these classes. The notions of quasi rack and derived solution are introduced and examined, extending the classical definitions. Additionally, a family of quasi left non-degenerate solutions is described in terms of quasi racks and g-twists, analogous to the left non-degenerate case. Furthermore, we completely characterize a class of quasi racks that are Plonka sum of racks. |
| title | Quasi racks, quasi bijective and quasi non-degenerate set-theoretic solutions of the Yang-Baxter equation |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2512.04215 |