On the new representation of the virtual braid group

摘要

We propose a representation of the virtual braid groupV Bn into the automorphism group of a free product of a free groupsand a free Abelian groups. V. G. Bardakov, Yu. A. Mikhalchishina andM. V. Neshchadim proposed a representation φM of the virtual braidgroup V Bn into the automorphism group of a free product of a freegroup and a free Abelian group. Our representation generalizes thisrepresentation φM. It is proved that the kernel of new representationis contained in the kernel of representation φM. It is proved that naturalgenetic code of image of the virtual braid group V Bn with respect tonew representation has strong symmetry.