67 citations · 246 across the 43 of their papers we have counts for
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Rota-Baxter operators on a sum of fields
Vsevolod Gubarev
We count the number of all Rota-Baxter operators on a finite direct sum of fields and count all of them up to conjugation with an automorphism…
Rota-Baxter operators and Bernoulli polynomials
Vsevolod Gubarev
We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter oper…
Embedding of post-Lie algebras into postassociative algebras
Vsevolod Gubarev
Applying Groebner-Shirshov technique, we prove that any post-Lie algebra injectively embeds into its universal enveloping postassociative algebra.
-polynomial of graph
Vsevolod Gubarev
We define -polynomial of graph which is related to clique, (in)dependence and matching polynomials. The growth rate of partially commutative monoid is equal to the largest root…
Embedding of pre-Lie algebras into preassociative algebras
Vsevolod Gubarev
With the help of Rota-Baxter operators and the Groebner-Shirshov bases, we prove that any pre-Lie algebra injectively embeds into its universal enveloping preassociative algebra.
Rota--Baxter operators and post-Lie algebra structures on semisimple Lie algebras
Dietrich Burde, Vsevolod Gubarev
Rota--Baxter operators of weight on are in bijective correspondence to post-Lie algebra structures on pairs , where $\mathfrak{n…
Rota-Baxter operators on unital algebras
Vsevolod Gubarev
We state that all Rota-Baxter operators of nonzero weight on Grassmann algebra over a field of characteristic zero are projections on a subalgebra along another one. We show the on…
Rota-Baxter Operators on Quadratic Algebras
Pilar Benito, Vsevolod Gubarev, Alexander Pozhidaev
We prove that all Rota-Baxter operators on a quadratic division algebra are trivial. For nonzero weight, we state that all Rota-Baxter operators on the simple odd-dimensional Jorda…