Реферат: 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.

Библиографическая ссылка: 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

Даты:

Поступила в редакцию:	17 июл. 2024 г.
Принята к публикации:	3 окт. 2024 г.
Опубликована в печати:	28 нояб. 2024 г.
Опубликована online:	28 нояб. 2024 г.

Идентификаторы БД:

Web of science:	WOS:001368240300002
РИНЦ:	74920365
OpenAlex:	W4404747404

Цитирование в БД: Пока нет цитирований

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