Isotopes of biracks and Zhang twists of algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917121478361088 |
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| author | Yu, Xiaolan Zhang, Yanfei |
| author_facet | Yu, Xiaolan Zhang, Yanfei |
| contents | In this paper, we introduce the notion of an $\mathbb{N}^p$-graded birack and construct its isotope. Every involutive $\mathbb{N}^p$-graded birack gives rise to an $\mathbb{N}^p$-graded Yang-Baxter algebra. We study the relation between isotopes of involutive $\mathbb{N}^p$-graded biracks and Zhang twists of $\mathbb{N}^p$-graded Yang-Baxter algebras. As an example, Yang-Baxter algebras determined by distributive solutions are proved to be Zhang twists of polynomial algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isotopes of biracks and Zhang twists of algebras Yu, Xiaolan Zhang, Yanfei Rings and Algebras In this paper, we introduce the notion of an $\mathbb{N}^p$-graded birack and construct its isotope. Every involutive $\mathbb{N}^p$-graded birack gives rise to an $\mathbb{N}^p$-graded Yang-Baxter algebra. We study the relation between isotopes of involutive $\mathbb{N}^p$-graded biracks and Zhang twists of $\mathbb{N}^p$-graded Yang-Baxter algebras. As an example, Yang-Baxter algebras determined by distributive solutions are proved to be Zhang twists of polynomial algebras. |
| title | Isotopes of biracks and Zhang twists of algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2512.03384 |