TY - JOUR

T1 - Representations of flat virtual braids which do not preserve the forbidden relations

AU - Bardakov, V.

AU - Chuzhinov, B.

AU - Emel'yanenkov, I.

AU - Ivanov, M.

AU - Markhinina, E.

AU - Nasybullov, T.

AU - Panov, S.

AU - Singh, N.

AU - Vasyutkin, S.

AU - Yakhin, V.

AU - Vesnin, A.

N1 - Публикация для корректировки.

PY - 2023/12

Y1 - 2023/12

N2 - In the paper, we construct a representation $\theta:FVB_n\to{\rm Aut}(F_{2n})$ 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 $\theta$.

AB - In the paper, we construct a representation $\theta:FVB_n\to{\rm Aut}(F_{2n})$ 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 $\theta$.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85186938742&origin=inward&txGid=8f4bccdf38d6abb6aaf35bb1fcd317f1

UR - http://arxiv.org/abs/2010.03162

UR - https://www.mendeley.com/catalogue/b50ce3da-8235-368a-8970-a0d38efe5c87/

U2 - 10.1142/S0218216523500931

DO - 10.1142/S0218216523500931

M3 - Article

VL - 32

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 14

M1 - 2350093

ER -