34 citations · 69 across the 7 of their papers we have counts for
8 papers
Rota-Baxter operators of non-scalar weights, connections with coboundary Lie bialgebra structures
Maxim Goncharov
In the paper, we introduce the notion of a Rota-Baxter operator of a non-scalar weight. As a motivation, we show that there is a natural connection between Rota-Baxter operators of…
From Rota-Baxter operators to quasitriangular Lie bialgebra structures on
Maxim Goncharov
In the paper we describe structures of quasitriangular Lie bialgebra on using the classification of Rota-Baxter operators of nonzero weight on .
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…
Rota-Baxter operators on cocommutative Hopf algebras
Maxim Goncharov
We generalize the notion of a Rota-Baxter operator on groups and the notion of a Rota-Baxter operator of weight 1 on Lie algebras and define and study the notion of a Rota-Baxter o…
Rota-Baxter operators of nonzero weight on the matrix algebra of order three
Maxim Goncharov, Vsevolod Gubarev
We classify all Rota-Baxter operators of nonzero weight on the matrix algebra of order three over an algebraically closed field of characteristic zero which are not arisen from the…
Rota-Baxter operators and non-skew-symmetric solutions of the classical Yang-Baxter equation on quadratic Lie algebras
Maxim Goncharov
We study possible connections between Rota-Baxter operators of non-zero weight and non-skew-symmetric solutions of the classical Yang-Baxter equation on finite-dimensional quadrati…
On Rota-Baxter operators of non-zero weight induced by non skew-symmetric solutions of the classical Yang-baxter equation on simple anticommutative algebras
M. E. Goncharov
Let be a simple anti-commutative algebra. In this paper we prove that a non skew-symmetric solution of the classical Yang-Baxter equation on with -invariant symmetric pa…
Simple finite-dimensional double algebras
M. E. Goncharov, P. S. Kolesnikov
A double algebra is a linear space equipped with linear map . Additional conditions on this map lead to the notions of Lie and associative double alge…