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VIRTUAL BRAIDS AND CLUSTER ALGEBRAS. / Егоров, Андрей Александрович.

In: Вестник Томского государственного университета. Математика и механика, Vol. 91, 2024, p. 18-30.

Research output: Contribution to journal › Article › peer-review

Harvard

Егоров, АА 2024, 'VIRTUAL BRAIDS AND CLUSTER ALGEBRAS', Вестник Томского государственного университета. Математика и механика, vol. 91, pp. 18-30. https://doi.org/10.17223/19988621/91/2

APA

Егоров, А. А. (2024). VIRTUAL BRAIDS AND CLUSTER ALGEBRAS. Вестник Томского государственного университета. Математика и механика, 91, 18-30. https://doi.org/10.17223/19988621/91/2

Vancouver

Егоров АА. VIRTUAL BRAIDS AND CLUSTER ALGEBRAS. Вестник Томского государственного университета. Математика и механика. 2024;91:18-30. doi: 10.17223/19988621/91/2

Author

Егоров, Андрей Александрович. / VIRTUAL BRAIDS AND CLUSTER ALGEBRAS. In: Вестник Томского государственного университета. Математика и механика. 2024 ; Vol. 91. pp. 18-30.

BibTeX

@article{3315e0f3dc914f5fa0d2a6f26a33779d,
title = "VIRTUAL BRAIDS AND CLUSTER ALGEBRAS",
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 FBn and the flat virtual braid group FVBn.",
keywords = "BRAID GROUP, CLUSTER ALGEBRA, VIRTUAL BRAID GROUP",
author = "Егоров, {Андрей Александрович}",
note = "Egorov, A. A. Virtual braids and cluster algebras / A. A. Egorov // Tomsk State University Journal of Mathematics and Mechanics. – 2024. – No. 91. – P. 18-30. – DOI 10.17223/19988621/91/2. ",
year = "2024",
doi = "10.17223/19988621/91/2",
language = "English",
volume = "91",
pages = "18--30",
journal = "Вестник Томского государственного университета. Математика и механика",
issn = "1998-8621",
publisher = "Издательство: Национальный исследовательский Томский государственный университет",

}

RIS

TY - JOUR

T1 - VIRTUAL BRAIDS AND CLUSTER ALGEBRAS

AU - Егоров, Андрей Александрович

N1 - Egorov, A. A. Virtual braids and cluster algebras / A. A. Egorov // Tomsk State University Journal of Mathematics and Mechanics. – 2024. – No. 91. – P. 18-30. – DOI 10.17223/19988621/91/2.

PY - 2024

Y1 - 2024

N2 - 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 FBn and the flat virtual braid group FVBn.

AB - 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 FBn and the flat virtual braid group FVBn.

KW - BRAID GROUP

KW - CLUSTER ALGEBRA

KW - VIRTUAL BRAID GROUP

UR - https://www.elibrary.ru/item.asp?id=74920365

U2 - 10.17223/19988621/91/2

DO - 10.17223/19988621/91/2

M3 - Article

VL - 91

SP - 18

EP - 30

JO - Вестник Томского государственного университета. Математика и механика

JF - Вестник Томского государственного университета. Математика и механика

SN - 1998-8621

ER -

ID: 67756772