On the new representation of the virtual braid group

Korobov Alexei Alexandrovich; Korobov Oleg Alexeevich

doi:10.33048/semi.2019.16.056

On the new representation of the virtual braid group

Korobov Alexei Alexandrovich, Korobov Oleg Alexeevich

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

Abstract

We propose a representation of the virtual braid group V B_n into the automorphism group of a free product of a free groups and a free Abelian groups. V. G. Bardakov, Yu. A. Mikhalchishina and M. V. Neshchadim proposed a representation ϕ_M of the virtual braid group V B_n into the automorphism group of a free product of a free group and a free Abelian group. Our representation generalizes this representation ϕ_M. It is proved that the kernel of new representation is contained in the kernel of representation ϕ_M. It is proved that natural genetic code of image of the virtual braid group V B_n with respect to new representation has strong symmetry

Translated title of the contribution	О новом представлении группы виртуальных кос
Original language	English
Pages (from-to)	863-875
Number of pages	13
Journal	Сибирские электронные математические известия
Volume	16
DOIs	https://doi.org/10.33048/semi.2019.16.056
Publication status	Published - 1 Jan 2019

Keywords

braids
virtual braids
representations by automorphisms
ALEXANDER GROUPS

OECD FOS+WOS

1.01 MATHEMATICS

State classification of scientific and technological information

27.17 Algebra

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10.33048/semi.2019.16.056

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title = "On the new representation of the virtual braid group",

abstract = "We propose a representation of the virtual braid group V Bn into the automorphism group of a free product of a free groups and a free Abelian groups. V. G. Bardakov, Yu. A. Mikhalchishina and M. V. Neshchadim proposed a representation ϕM of the virtual braid group V Bn into the automorphism group of a free product of a free group and a free Abelian group. Our representation generalizes this representation ϕM. It is proved that the kernel of new representation is contained in the kernel of representation ϕM. It is proved that natural genetic code of image of the virtual braid group V Bn with respect to new representation has strong symmetry",

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KW - Braids

KW - Representations by automorphisms

KW - Virtual braids

KW - braids

KW - virtual braids

KW - representations by automorphisms

KW - ALEXANDER GROUPS

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On the new representation of the virtual braid group

Abstract

Keywords

OECD FOS+WOS

State classification of scientific and technological information

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