Garsideness properties of structure groups of set-theoretic solutions of the Yang-Baxter equation
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912142038401024 |
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| author | Chouraqui, Fabienne |
| author_facet | Chouraqui, Fabienne |
| contents | There exists a multiplicative homomorphism from the braid group B to the Temperley-Lieb algebra TL. Moreover, the homomorphic images in TL of the simple elements form a basis for the vector space underlying TL. In analogy with the case of B, there exists a multiplicative homomorphism from the structure group G of a non-degenerate, involutive set-theoretic solution to an algebra, which extends to a homomorphism of algebras. We construct a finite basis of the underlying vector space of the image of G using the Garsideness properties of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_03176 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Garsideness properties of structure groups of set-theoretic solutions of the Yang-Baxter equation Chouraqui, Fabienne Group Theory Quantum Algebra Rings and Algebras 20F05, 20F65, 20C07 There exists a multiplicative homomorphism from the braid group B to the Temperley-Lieb algebra TL. Moreover, the homomorphic images in TL of the simple elements form a basis for the vector space underlying TL. In analogy with the case of B, there exists a multiplicative homomorphism from the structure group G of a non-degenerate, involutive set-theoretic solution to an algebra, which extends to a homomorphism of algebras. We construct a finite basis of the underlying vector space of the image of G using the Garsideness properties of the solution. |
| title | Garsideness properties of structure groups of set-theoretic solutions of the Yang-Baxter equation |
| topic | Group Theory Quantum Algebra Rings and Algebras 20F05, 20F65, 20C07 |
| url | https://arxiv.org/abs/2206.03176 |