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Представления групп виртуальных и сингулярных кос. / Козловская, Татьяна Анатольевна; Соколов, Павел Петрович.

In: Сибирские электронные математические известия, Vol. 22, No. 1, 2025, p. 701-734.

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

Harvard

Козловская, ТА & Соколов, ПП 2025, 'Представления групп виртуальных и сингулярных кос', Сибирские электронные математические известия, vol. 22, no. 1, pp. 701-734. https://doi.org/10.33048/semi.2025.22.047

APA

Козловская, Т. А., & Соколов, П. П. (2025). Представления групп виртуальных и сингулярных кос. Сибирские электронные математические известия, 22(1), 701-734. https://doi.org/10.33048/semi.2025.22.047

Vancouver

Козловская ТА, Соколов ПП. Представления групп виртуальных и сингулярных кос. Сибирские электронные математические известия. 2025;22(1):701-734. doi: 10.33048/semi.2025.22.047

Author

Козловская, Татьяна Анатольевна ; Соколов, Павел Петрович. / Представления групп виртуальных и сингулярных кос. In: Сибирские электронные математические известия. 2025 ; Vol. 22, No. 1. pp. 701-734.

BibTeX

@article{9930d99e672e4d2497c919ba26fef720,
title = "Представления групп виртуальных и сингулярных кос",
abstract = "In the present paper, we study various representations of the virtual braid group V Bn, the singular braid monoid SMn, and the singular braid group SBn. We construct a representation of the virtual braid group into the group of automorphisms of the quandle. We prove that this representation generalizes some wellknown representations. Using this representation, we construct an invariant of virtual links. Also we investigate representations of the singular braid monoid SMn and the singular braid group SBn by endomorphisms and automorphisms of a free module and a free group. In particular, we find all linear local homogeneous representations of the singular braid monoid that extend the Burau representation of the braid group and find conditions under which these representations can be extended to the group SBn. We prove that the constructed linear representation is reducible and an irreducible representation is obtained that extends the reduced Burau representation.",
keywords = "virtual braid group, singular braid group, Burau repre sentation, knot, link, quandle, Burau representation",
author = "Козловская, {Татьяна Анатольевна} and Соколов, {Павел Петрович}",
note = "Козловская Т. А., Соколов П. П. Представления групп виртуальных и сингулярных кос / Т. А. Козловская, П. П. Соколов // Сибирские электронные математические известия. – 2025. – Т. 22, № 1. – С. 701-734. – DOI 10.33048/semi.2025.22.047",
year = "2025",
doi = "10.33048/semi.2025.22.047",
language = "русский",
volume = "22",
pages = "701--734",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "1",

}

RIS

TY - JOUR

T1 - Представления групп виртуальных и сингулярных кос

AU - Козловская, Татьяна Анатольевна

AU - Соколов, Павел Петрович

N1 - Козловская Т. А., Соколов П. П. Представления групп виртуальных и сингулярных кос / Т. А. Козловская, П. П. Соколов // Сибирские электронные математические известия. – 2025. – Т. 22, № 1. – С. 701-734. – DOI 10.33048/semi.2025.22.047

PY - 2025

Y1 - 2025

N2 - In the present paper, we study various representations of the virtual braid group V Bn, the singular braid monoid SMn, and the singular braid group SBn. We construct a representation of the virtual braid group into the group of automorphisms of the quandle. We prove that this representation generalizes some wellknown representations. Using this representation, we construct an invariant of virtual links. Also we investigate representations of the singular braid monoid SMn and the singular braid group SBn by endomorphisms and automorphisms of a free module and a free group. In particular, we find all linear local homogeneous representations of the singular braid monoid that extend the Burau representation of the braid group and find conditions under which these representations can be extended to the group SBn. We prove that the constructed linear representation is reducible and an irreducible representation is obtained that extends the reduced Burau representation.

AB - In the present paper, we study various representations of the virtual braid group V Bn, the singular braid monoid SMn, and the singular braid group SBn. We construct a representation of the virtual braid group into the group of automorphisms of the quandle. We prove that this representation generalizes some wellknown representations. Using this representation, we construct an invariant of virtual links. Also we investigate representations of the singular braid monoid SMn and the singular braid group SBn by endomorphisms and automorphisms of a free module and a free group. In particular, we find all linear local homogeneous representations of the singular braid monoid that extend the Burau representation of the braid group and find conditions under which these representations can be extended to the group SBn. We prove that the constructed linear representation is reducible and an irreducible representation is obtained that extends the reduced Burau representation.

KW - virtual braid group

KW - singular braid group

KW - Burau repre sentation

KW - knot

KW - link

KW - quandle

KW - Burau representation

UR - https://math-semr.ru/sites/math-semr.ru/files/2025-07/p0701-0734.pdf

UR - https://www.mendeley.com/catalogue/32693407-d4ad-3eff-8bc6-85e2523a6e8a/

U2 - 10.33048/semi.2025.22.047

DO - 10.33048/semi.2025.22.047

M3 - статья

VL - 22

SP - 701

EP - 734

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 1

ER -

ID: 71568599