output
20152022
most citedRota-Baxter groups, skew left braces, and the Yang-Baxter equation

51 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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math.GR2021★ 25 cited

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…

math.GR2021★ 51 cited

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…

math.GR2018★ 3 cited

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…

math.GR2017★ 18 cited

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…

math.GR2017★ 4 cited

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…

math.GR2016★ 24 cited

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…

math.GR2015

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…