V. Gubarev

activity

20092026

most citedOn embedding of dendriform algebras into Rota---Baxter algebras

67 citations · 246 across the 43 of their papers we have counts for

collaborators

50 papers

math.RA2026

A simple construction of a simple nil ring

Vsevolod Gubarev

In 1999, A. Smoktunowicz solved a long-standing problem and constructed a simple nil ring. We present a substantial simplification of this construction found by Aristotle (Harmonic…

math.RA2026

Extremal Rota-Baxter operators on matrix algebras

Vsevolod Gubarev

We classify all Rota-Baxter operators of weight $λ$ on $M_{n} (F)$ over a field $F$ of characteristic zero whose minimal polynomial has maximal degree and show that in both cases $λ=…

math.RA2026

Failure of Ado-type theorems for preLie and postLie algebras

Vsevolod Gubarev

Over an arbitrary field of characteristic zero, we construct a two-dimensional preLie algebra and a two-dimensional postLie algebra that do not embed into the corresponding induced…

math.RA2026

Simple double Lie algebras on the Laurent polynomial space

Vsevolod Gubarev

We construct a simple $λ$ -double Lie algebra on $k [t, t^{- 1}]$ for every nonzero $λ \in k$ . We then show that the analogous two-sided construction of weight zero is also simple. Both…

math.RA2026

Injective Rota-Baxter operators of weight 1 on $F [x]$

Vsevolod Gubarev

We describe all injective Rota-Baxter operators $R$ of weight 1 on the polynomial algebra $F [x]$ . When $char F = p > 0$ , the only one is $R = - id$ . When $\mathrm{cha…

math.RA2026

Inner post-Lie algebras and inner post-groups

V. Gubarev, Y. Li, Y. Sheng +1

In this paper, using extension theory and cohomological approach we introduce the notion of the obstruction class for an inner post-Lie algebra being induced by a Rota-Baxter opera…

math.RA2026

Free Poisson Rota-Baxter algebra

Vsevolod Gubarev

We construct a free Poisson algebra endowed with a Rota-Baxter operator. The same construction works for a free Poisson algebra endowed with a Nijenhuis operator.

math.GR2025

On Rota--Baxter operators on finite simple groups of Lie type

Alexey Galt, Vsevolod Gubarev

Rota--Baxter operators on groups were introduced by L. Guo, H. Lang, Yu. Sheng in 2020. In 2023, V. Bardakov and the second author showed that all Rota--Baxter operators on simple…

math.RA2025★ 1 cited

Rota-Baxter operators on the simple Jordan algebra of matrices of order two

Vsevolod Gubarev, Alexander Panasenko

We describe all Rota-Baxter operators of any weight on the space of matrices from $M_{2} (F)$ considered under the product $a \circ b = (ab + ba) /2$ and usually denoted as $M_2(F)^{(+)…

math.RA2024★ 1 cited

Rota-Baxter operators of weight zero on the matrix algebra of order three without unit in kernel

Vsevolod Gubarev

We describe all Rota-Baxter operators $R$ of weight zero on the matrix algebra $M_{3} (F)$ over a quadratically closed field $F$ of characteristic not 2 or 3 such that $R (1) \neq = 0$ . Th…

math.GR2024

Rota-Baxter operators on dihedral and alternating groups

Alexey Galt, Vsevolod Gubarev

Rota-Baxter operators on algebras, which appeared in 1960, have connections with different versions of the Yang-Baxter equation, pre- and postalgebras, double Poisson algebras, etc…

math.RA2024★ 3 cited

Rota-Baxter operators of weight zero on upper-triangular matrices of order three

Vsevolod Gubarev

We describe all Rota-Baxter operators $R$ of weight zero on the algebra $U_{3} (F)$ of upper-triangular matrices of order three over a field of characteristic 0. For this, we apply th…

math.RA2023★ 1 cited

Burde's series of simple pre-Lie algebras

Vsevolod Gubarev

We describe automorphisms, derivations, and Rota -- Baxter operators on the series of simple pre-Lie algebras found by D. Burde in 1998.

math.RA2023★ 4 cited

Nonunital decompositions of the matrix algebra of order three

Vsevolod Gubarev

All decompositions of $M_{3} (C)$ into a direct vector-space sum of two subalgebras such that none of the subalgebras contains the identity matrix are classified. Thus, the c…

math.RA2023

Generalized sharped cubic form and split spin factor algebra

Vsevolod Gubarev, Farukh Mashurov, Alexander Panasenko

There is a well-known construction of a Jordan algebra via a sharped cubic form. We introduce a generalized sharped cubic form and prove that the split spin factor algebra is induc…

math.RA2022

Rota-Baxter operators on $Cur (sl_{2} (C))$

Vsevolod Gubarev, Roman Kozlov

We classify all Rota-Baxter operators on the simple conformal Lie algebra $Cur (sl_{2} (C))$ and clarify which of them arise from the solutions to the confor…

math.QA2022

Conformal Yang-Baxter equation on $Cur (sl_{2} (C))$

Vsevolod Gubarev, Roman Kozlov

In 2008, J. Liberati defined what is a conformal Lie bialgebra and introduced the conformal classical Yang-Baxter equation (CCYBE). An $L$ -invariant solution to the weak version of…

math.RA2022

Free special Gelfand-Dorfman algebra

V. Gubarev, B. K. Sartayev

A Gelfand-Dorfman algebra is called special if it can be embedded into a differential Poisson algebra. We find a new basis of the free Novikov algebra. With its help, we construct…

math.RA2022

Quasi-definite axial algebras of Jordan type half

Ilya Gorshkov, Vsevolod Gubarev

Axial algebras are commutative nonassociative algebras generated by a finite set of primitive idempotents which action on an algebra is semisimple, and the fusion laws on the produ…

math.RA2021★ 2 cited

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.…

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.RA2021

Double Lie algebras of a nonzero weight

Maxim Goncharov, Vsevolod Gubarev

We introduce the notion of $λ$ -double Lie algebra, which coincides with usual double Lie algebra when $λ = 0$ . We state that every $λ$ -double Lie algebra for $λ \neq = 0$ provides the s…

math.RA2021★ 1 cited

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…

A simple construction of a simple nil ring

Extremal Rota-Baxter operators on matrix algebras

Failure of Ado-type theorems for preLie and postLie algebras

Simple double Lie algebras on the Laurent polynomial space

Injective Rota-Baxter operators of weight 1 on F[x]

Inner post-Lie algebras and inner post-groups

Free Poisson Rota-Baxter algebra

On Rota--Baxter operators on finite simple groups of Lie type

Rota-Baxter operators on the simple Jordan algebra of matrices of order two

Rota-Baxter operators of weight zero on the matrix algebra of order three without unit in kernel

Rota-Baxter operators on dihedral and alternating groups

Rota-Baxter operators of weight zero on upper-triangular matrices of order three

Burde's series of simple pre-Lie algebras

Nonunital decompositions of the matrix algebra of order three

Generalized sharped cubic form and split spin factor algebra

Rota-Baxter operators on Cur(sl2​(C))

Conformal Yang-Baxter equation on Cur(sl2​(C))

Free special Gelfand-Dorfman algebra

Quasi-definite axial algebras of Jordan type half

Universal enveloping algebra of a pair of compatible Lie brackets

Rota-Baxter operators on groups

Rota-Baxter groups, skew left braces, and the Yang-Baxter equation

Double Lie algebras of a nonzero weight

An example of a simple double Lie algebra

Injective Rota-Baxter operators of weight 1 on $F [x]$

Rota-Baxter operators on $Cur (sl_{2} (C))$

Conformal Yang-Baxter equation on $Cur (sl_{2} (C))$