51 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Sobolev Institute of MathematicsRU13 papers
- Novosibirsk State UniversityRU12 papers
- Indian Institute of Science Education and Research MohaliIN9 papers
- National Research Tomsk State UniversityRU7 papers
- Chelyabinsk State UniversityRU3 papers
- Harish-Chandra Research InstituteIN1 paper
- Lomonosov Moscow State UniversityRU1 paper
- Panjab UniversityIN1 paper
- Yaroslavl State UniversityRU1 paper
13 papers
Extensions of Yang-Baxter sets
Valeriy G. Bardakov, Dmitry V. Talalaev
The paper extends the notion of braided set and its close relative - the Yang-Baxter set - to the category of vector spaces and explore structure aspects of such a notion as morphi…
Rota-Baxter operators on groups
Valeriy G. Bardakov, Vsevolod Gubarev
Theory of Rota-Baxter operators on rings and algebras has been developed since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined the notion of Rota-Baxter o…
Rota-Baxter groups, skew left braces, and the Yang-Baxter equation
Valeriy G. Bardakov, Vsevolod Gubarev
Braces were introduced by W. Rump in 2006 as an algebraic system related to the quantum Yang-Baxter equation. In 2017, L. Guarnieri and L. Vendramin defined for the same purposes a…
Virtually Symmetric representations and marked Gauss diagrams
Valeriy G. Bardakov, Mikhail V. Neshchadim, Manpreet Singh
In this paper, we define the notion of a virtually symmetric representation of representations of virtual braid groups and prove that many known representations are equivalent to v…
Quandle cohomology, extensions and automorphisms
Valeriy Bardakov, Mahender Singh
The paper establishes new relationship between cohomology, extensions and automorphisms of quandles. We derive a four term exact sequence relating quandle 1-cocycles, second quandl…
Computing skew left braces of small orders
Valeriy G. Bardakov, Mikhail V. Neshchadim, Manoj K. Yadav
We improve Algorithm 5.1 of [Math. Comp. {\bf 86} (2017), 2519-2534] for computing all non-isomorphic skew left braces, and enumerate left braces and skew left braces of orders up…
Link quandles are residually finite
Valeriy G. Bardakov, Mahender Singh, Manpreet Singh
Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of…
On the lower central series of some virtual knot groups
Valeriy G. Bardakov, Neha Nanda, Mikhail V. Neshchadim
We study groups of some virtual knots with small number of crossings and prove that there is a virtual knot with long lower central series which, in particular, implies that there…
Exterior and symmetric (co)homology of groups
Valeriy G. Bardakov, Mikhail V. Neshchadim, Mahender Singh
The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite g…
Quandle rings
Valeriy G. Bardakov, Inder Bir Singh Passi, Mahender Singh
In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated…
Automorphisms of pure braid Groups
Valeriy G. Bardakov, Mikhail V. Neshchadim, Mahender Singh
In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for , $\Aut(P_n)$ is generated by the subgroup $\Aut_c(P_n)$ of cen…
Automorphism groups of quandles arising from groups
Valeriy G. Bardakov, Pinka Dey, Mahender Singh
Let be a group and $φ\in \Aut(G)$. Then the set equipped with the binary operation gives a quandle structure on , denoted by $\Alex(G, φ)$ and called t…
Palindromic Automorphisms of Free Nilpotent Groups
Valeriy G. Bardakov, Krishnendu Gongopadhyay, Mikhail V. Neshchadim +1
In this paper, we initiate the study of palindromic automorphisms of groups that are free in some variety. More specifically, we define palindromic automorphisms of free nilpotent…