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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 863–875 (Mi semr1098)  

Mathematical logic, algebra and number theory

On the new representation of the virtual braid group

A. A. Korobova, O. A. Korobovb

a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia
b Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia

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 $\varphi_{M}$ 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 $\varphi_{M}$. It is proved that the kernel of new representation is contained in the kernel of representation $\varphi_{M}$. 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.

Keywords: braids, virtual braids, representations by automorphisms.

DOI: https://doi.org/10.33048/semi.2019.16.056

Full text: PDF file (184 kB)
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Bibliographic databases:

UDC: 512.8
MSC: 20F36+20F05+20F10
Received November 5, 2018, published June 14, 2019

Citation: A. A. Korobov, O. A. Korobov, “On the new representation of the virtual braid group”, Sib. Èlektron. Mat. Izv., 16 (2019), 863–875

Citation in format AMSBIB
\Bibitem{KorKor19}
\by A.~A.~Korobov, O.~A.~Korobov
\paper On the new representation of the virtual braid group
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 863--875
\mathnet{http://mi.mathnet.ru/semr1098}
\crossref{https://doi.org/10.33048/semi.2019.16.056}


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