1 citations · 1 across the 12 of their papers we have counts for
14 papers
Multi-virtual braid groups
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Komal Negi +1
L. Kauffman (2024) introduced multi-virtual and symmetric multi-virtual braid groups, which are generalizations of the virtual braid group. We introduce multi-virtual pure and mult…
Cayley graphs and their growth functions for multivalued groups
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Matvei N. Zonov
We define the Cayley graph and its growth function for multivalued groups. We prove that if we change a finite set of generators of multivalued group, or change the starting point,…
Extensions of braid group representations to the monoid of singular braids
Valeriy G. Bardakov, Nafaa Chbili, Tatyana A. Kozlovskaya
Given a representation of the braid group , into a group , we are considering the problem of whether it is possible to extend this repres…
Multi-groups
Tatyana A. Kozlovskaya
In the present paper we define homogeneous algebraic systems. Particular cases of these systems are: semigroup (monoid, group) system. These algebraic systems were studied by J. Lo…
n-valued quandles and associated bialgebras
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Dmitry V. Talalaev
The principal aim of this article is to introduce and study n-valued quandles and n-corack bialgebras. We elaborate the basic methods of this theory, reproduce the coset constructi…
Twisted Virtual Braid Group
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Komal Negi +1
In this paper we study some subgroups and their decompositions in semi-direct product of the twisted virtual braid group . In particular, the twisted virtual pure braid grou…
Multivalued groups and Newton polyhedron
Valeriy G. Bardakov, Tatyana A. Kozlovskaya
On the set of complex number it is possible to define -valued group for any positive integer . The -multiplication defines a symmetric polynomial $p_n = p_n(x…
Links and dynamics
Valeriy Bardakov, Tatyana Kozlovskaya, Olga Pochinka
Knots naturally appear in continuous dynamical systems as flow periodic trajectories. However, discrete dynamical systems are also closely connected with the theory of knots and li…
Singular braids, singular links and subgroups of camomile type
Valeriy G. Bardakov, Tatyana A. Kozlovskaya
In this paper we find a finite set of generators and defining relations for the singular pure braid group , , that is a subgroup of the singular braid group .…
Virtual and universal braid groups, their quotients and representations
V. Bardakov, I. Emel'yanenkov, M. Ivanov +3
In the present paper we study structural aspects of certain quotients of braid groups and virtual braid groups. In particular, we construct and study linear representations $B_n\to…
On some decompositions of the 3-strand Singular Braid Group
Krishnendu Gongopadhyay, Tatyana A. Kozlovskaya, Oleg V. Mamonov
Let be the singular braid group generated by braid generators and singular braid generators , . Let denote the group that is the kernel…
On 3-strand singular pure braid group
Valeriy G. Bardakov, Tatyana A. Kozlovskaya
In the present paper we study the singular pure braid group for . We find generators, defining relations and the algebraical structure of these groups. In particul…
Brieskorn manifolds, generalised Sieradski groups, and coverings of lens spaces
Tatyana Kozlovskaya, Andrei Vesnin
The Brieskorn manifolds are the -fold cyclic coverings of the 3-sphere branched over the torus knot . The generalised Sieradski groups are…
Cyclic generalizations of two hyperbolic icosahedral manifolds
P. Cristofori, T. Kozlovskaya, A. Vesnin
We discuss two families of closed orientable three-dimensional manifolds which arise as cyclic generalizations of two hyperbolic icosahedral manifolds listed by Everitt. Everitt's…