Representations of Flat Virtual Braids by Automorphisms of Free Group Full article
| Journal |
Symmetry
ISSN: 2073-8994 |
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| Output data | Year: 2023, Volume: 15, Number: 8, Article number : 1538, Pages count : 19 DOI: 10.3390/sym15081538 | ||||
| Tags | braid; virtual braid; flat virtual braid group; automorphism of free group | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
Representations of braid group Bn on n≥2 strands by automorphisms of a free group of rank n go back to Artin. In 1991, Kauffman introduced a theory of virtual braids, virtual knots, and links. The virtual braid group VBn on n≥2 strands is an extension of the classical braid group Bn by the symmetric group Sn. In this paper, we consider flat virtual braid groups FVBn on n≥2 strands and construct a family of representations of FVBn by automorphisms of free groups of rank 2n. It has been established that these representations do not preserve the forbidden relations between classical and virtual generators. We investigated some algebraic properties of the constructed representations. In particular, we established conditions of faithfulness in case n=2 and proved that the kernel contains a free group of rank two for n≥3.
Cite:
Chuzhinov B.
, Vesnin A.
Representations of Flat Virtual Braids by Automorphisms of Free Group
Symmetry. 2023. V.15. N8. 1538 :1-19. DOI: 10.3390/sym15081538 WOS Scopus РИНЦ OpenAlex
Representations of Flat Virtual Braids by Automorphisms of Free Group
Symmetry. 2023. V.15. N8. 1538 :1-19. DOI: 10.3390/sym15081538 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jun 19, 2023 |
| Accepted: | Aug 1, 2023 |
| Published print: | Aug 3, 2023 |
| Published online: | Aug 3, 2023 |
Identifiers:
| Web of science: | WOS:001119090600001 |
| Scopus: | 2-s2.0-85168901087 |
| Elibrary: | 63480757 |
| OpenAlex: | W4385575815 |