51 citations · 254 across the 64 of their papers we have counts for
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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…
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…
A Wells type exact sequence for non-degenerate unitary solutions of the Yang--Baxter equation
Valeriy Bardakov, Mahender Singh
Cycle sets are known to give non-degenerate unitary solutions of the Yang--Baxter equation and linear cycle sets are enriched versions of these algebraic systems. The paper explore…