67 citations · 246 across the 43 of their papers we have counts for
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Universal enveloping algebra of a pair of compatible Lie brackets
Vsevolod Gubarev
Applying the Poincare-Birkhoff-Witt property and the Groebner-Shirshov bases technique, we find the linear basis of the associative universal enveloping algebra in the sense of V.…
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…
Double Lie algebras of a nonzero weight
Maxim Goncharov, Vsevolod Gubarev
We introduce the notion of -double Lie algebra, which coincides with usual double Lie algebra when . We state that every -double Lie algebra for provides the s…
An example of a simple double Lie algebra
Vsevolod Gubarev
We extend the correspondence between double Lie algebras and skew-symmetric Rota-Baxter operators of weight 0 on the matrix algebra for the infinite-dimensional case. We give the f…