RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Sib. Èlektron. Mat. Izv.: Year: Volume: Issue: Page: Find

 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)
References: PDF file   HTML file

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} `