Geodesic
On the new representation of the virtual braid group
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 863-875

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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. 
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     author = {A. A. Korobov and O. A. Korobov},
     title = {On the new representation of the virtual braid group},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {863--875},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a14/}
}
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A. A. Korobov; O. A. Korobov. On the new representation of the virtual braid group. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 863-875. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a14/