51 citations · 254 across the 64 of their papers we have counts for
6 papers · 1 filter
Brunnian planar braids and simplicial groups
Valeriy G. Bardakov, Pravin Kumar, Mahender Singh
Twin groups are planar analogues of Artin braid groups and play a crucial role in the Alexander-Markov correspondence for the isotopy classes of immersed circles on the 2-sphere wi…
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…
Relative Rota--Baxter operators on groups and Hopf algebras
Valeriy G. Bardakov, Igor M. Nikonov
M. Goncharov introduced and studied a Rota--Baxter operator on a cocommutative Hopf algebra. In the present paper we define relative Rota--Baxter operators on an arbitrary Hopf alg…
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…