Representations of flat virtual braids which do not preserve the forbidden relations Full article
| Journal |
Journal of Knot Theory and its Ramifications
ISSN: 0218-2165 |
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| Output data | Year: 2023, Volume: 32, Number: 4, Article number : 2350093, Pages count : 27 DOI: 10.1142/S0218216523500931 | ||||||||
| Tags | Flat virtual braids, braid-like groups, representations by automorphisms | ||||||||
| Authors |
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| Affiliations |
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Funding (3)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
| 2 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
| 3 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
In the paper, we construct a representation theta:FVB_n→{\rm Aut}(F_{2n})$ of the flat virtual braid group FVB_n on n strands by automorphisms of the free group F_{2n} with 2n generators which does not preserve the forbidden relations in the flat virtual braid group. This representation gives a positive answer to the problem formulated by V. Bardakov in the list of unsolved problems in virtual knot theory and combinatorial knot theory by R. Fenn, D. Ilyutko, L. Kauffman and V. Manturov. Using this representation we construct a new group invariant for flat welded links. Also we find the set of normal generators of the groups VP_n\cap H_n in VB_n, FVP_n\cap FH_n in FVB_n, GVP_n\cap GH_n in GVB_n, which play an important role in the study of the kernel of the representation theta.
Cite:
Bardakov V.
, Chuzhinov B.
, Emel'yanenkov I.
, Ivanov M.
, Markhinina E.
, Nasybullov T.
, Panov S.
, Singh N.
, Vasyutkin S.
, Yakhin V.
, Vesnin A.
Representations of flat virtual braids which do not preserve the forbidden relations
Journal of Knot Theory and its Ramifications. 2023. V.32. N4. 2350093 :1-27. DOI: 10.1142/S0218216523500931 WOS Scopus РИНЦ OpenAlex
Representations of flat virtual braids which do not preserve the forbidden relations
Journal of Knot Theory and its Ramifications. 2023. V.32. N4. 2350093 :1-27. DOI: 10.1142/S0218216523500931 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Oct 7, 2020 |
| Accepted: | Sep 20, 2023 |
| Published print: | Nov 25, 2023 |
| Published online: | Feb 27, 2024 |
Identifiers:
| Web of science: | WOS:001183905800005 |
| Scopus: | 2-s2.0-85186938742 |
| Elibrary: | 65181941 |
| OpenAlex: | W3092523305 |