Virtual braids and cluster algebras Full article
| Journal |
Вестник Томского государственного университета. Математика и механика (Vestnik Tomskogo Gosudarstvennogo Universiteta, Matematika i Mekhanika)
ISSN: 1998-8621 , E-ISSN: 2311-2255 |
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| Output data | Year: 2024, Number: 91, Pages: 18-30 Pages count : 13 DOI: 10.17223/19988621/91/2 | ||||||
| Tags | braid group, virtual braid group, cluster algebra | ||||||
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| Affiliations |
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Funding (1)
| 1 | Tomsk State University | НУ 2.0.1.23 ОНТ Приоритет-2030 |
Abstract:
In 2015, Hikami and Inoue constructed a representation of the braid group Bn in terms of cluster algebra associated with the decomposition of the complement of the corresponding knot into ideal hyperbolic tetrahedra. This representation leads to the calculation of the hyperbolic volume of the complement of the knot that is the closure of the corresponding braid. In this paper, based on the Hikami–Inoue representation discussed above, we construct a representation for the virtual braid group VBn. We show that the so-called “forbidden relations” do not hold in the image of the resulting representation. In addition, based on the developed method, we construct representations for the flat braid group FB n and the flat virtual braid group FVBn.
Cite:
Egorov A.A.
Virtual braids and cluster algebras
Вестник Томского государственного университета. Математика и механика (Vestnik Tomskogo Gosudarstvennogo Universiteta, Matematika i Mekhanika). 2024. N91. P.18-30. DOI: 10.17223/19988621/91/2 WOS РИНЦ OpenAlex
Virtual braids and cluster algebras
Вестник Томского государственного университета. Математика и механика (Vestnik Tomskogo Gosudarstvennogo Universiteta, Matematika i Mekhanika). 2024. N91. P.18-30. DOI: 10.17223/19988621/91/2 WOS РИНЦ OpenAlex
Dates:
| Submitted: | Jul 17, 2024 |
| Accepted: | Oct 3, 2024 |
| Published print: | Nov 28, 2024 |
| Published online: | Nov 28, 2024 |
Identifiers:
| Web of science: | WOS:001368240300002 |
| Elibrary: | 74920365 |
| OpenAlex: | W4404747404 |
Citing:
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