Parametric reflection maps: an algebraic approach
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908828129296384 |
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| author | Doikou, Anastasia Mazzotta, Marzia Stefanelli, Paola |
| author_facet | Doikou, Anastasia Mazzotta, Marzia Stefanelli, Paola |
| contents | We study solutions of the parametric set-theoretic reflection equation from an algebraic perspective by employing recently derived generalizations of the familiar shelves and racks, called parametric (p)-shelves and racks. Generic invertible solutions of the set-theoretic reflection equation are also obtained by a suitable parametric twist. The twist leads to considerably simplified constraints compared to the ones obtained from general set-theoretic reflections. In this context, novel algebraic structures of (skew) p-braces that generalize the known (skew) braces and are suitable for the parametric Yang-Baxter equation are introduced. The p-rack Yang-Baxter and reflection operators as well as the associated algebraic structures are defined setting up the frame for formulating the p-rack reflection algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15839 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parametric reflection maps: an algebraic approach Doikou, Anastasia Mazzotta, Marzia Stefanelli, Paola Rings and Algebras Mathematical Physics We study solutions of the parametric set-theoretic reflection equation from an algebraic perspective by employing recently derived generalizations of the familiar shelves and racks, called parametric (p)-shelves and racks. Generic invertible solutions of the set-theoretic reflection equation are also obtained by a suitable parametric twist. The twist leads to considerably simplified constraints compared to the ones obtained from general set-theoretic reflections. In this context, novel algebraic structures of (skew) p-braces that generalize the known (skew) braces and are suitable for the parametric Yang-Baxter equation are introduced. The p-rack Yang-Baxter and reflection operators as well as the associated algebraic structures are defined setting up the frame for formulating the p-rack reflection algebra. |
| title | Parametric reflection maps: an algebraic approach |
| topic | Rings and Algebras Mathematical Physics |
| url | https://arxiv.org/abs/2412.15839 |