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Representations of flat virtual braids which do not preserve the forbidden relations.
- Source :
-
Journal of Knot Theory & Its Ramifications . Dec2023, Vol. 32 Issue 14, p1-27. 27p. - Publication Year :
- 2023
-
Abstract
- In the paper, we construct a representation : FVB n → Aut (F 2 n) of the flat virtual braid group FVB n on n strands by automorphisms of the free group F 2 n with 2 n 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 Bardakov in the list of unsolved problems in virtual knot theory and combinatorial knot theory by Fenn et al. Also we find the set of normal generators of the groups VP n ∩ H n in VB n , FVP n ∩ FH n in FVB n , GVP n ∩ GH n in GVB n , which play an important role in the study of the kernel of the representation  . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 32
- Issue :
- 14
- Database :
- Academic Search Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 175725170
- Full Text :
- https://doi.org/10.1142/S0218216523500931