U. Umirbaev

activity

20062026

most citedIdentities of dual Leibniz algebras

14 citations · 44 across the 30 of their papers we have counts for

collaborators

41 papers

math.RA2026

Automorphisms of Free Metabelian Lie Algebras, II

Ualbai Umirbaev

We show that every automorphism of the free metabelian Lie algebra $M_{n}$ of rank $n \geq 4$ over an arbitrary field $K$ is almost tame; that is, it can be expressed as a product of…

math.RA2025

Chein Automorphisms of Free Metabelian Anticommutative Algebras

Ruslan Nauryzbaev, Ivan Shestakov, Ualbai Umirbaev

We describe all automorphisms of a free metabelian anticommutative algebra of rank $n \geq 3$ over a field $K$ that move only one variable while fixing the others. Such automorphism…

math.RT2025

Representations of the Grassmann Poisson superalgebras

Ivan Shestakov, Ualbai Umirbaev

We prove that every irreducible Poisson supermodule over the Grassmann Poisson superalgebra $G_{n}$ over a field of characteristic different from $2$ is isomorphic to the regular Poi…

math.RA2025

Tangent Lie Algebras of Automorphism Groups of Free Algebras

Ivan Shestakov, Ualbai Umirbaev

We study an analogue of the Andreadakis-Johnson filtration for automorphism groups of free algebras and introduce the notion of tangent Lie algebras for certain automorphism groups…

math.RA2025

Automorphisms and derivations of a universal left-symmetric enveloping algebra

D. Zhangazinova, A. Naurazbekova, U. Umirbaev

Let $A_{n}$ be an $n$ -dimensional algebra with zero multiplication over a field $K$ of characteristic $0$ . Then its universal (multiplicative) enveloping algebra $U_{n}$ in the variety…

math.RA2024

Automorphisms of free metabelian Lie algebras, I

Ualbai Umirbaev

We show that all Chein automorphisms (or one-row transformations) of lower degree $\geq 4$ of a free metabelian Lie algebra $M_{n}$ of rank $n \geq 4$ over an arbitrary field $K$ of c…

math.RA2024

Erroneous proofs of the wildness of some automorphisms of free metabelian Lie algebras

Ualbai Umirbaev

The well-known Bachmuth-Mochizuki-Roman'kov Theorem \cite{BM,Romankov85} states that every automorphism of the free metabelian group of rank $\geq 4$ is tame. In 1992 Yu. Bahturin…

math.RA2023

On a variety of right-symmetric algebras

Nurlan Ismailov, Ualbai Umirbaev

We construct a finite-dimensional metabelian right-symmetric algebra over an arbitrary field that does not have a finite basis of identities.

math.RA2023

Automorphisms of Veronese subalgebras of polynomial algebras and free Poisson algebras

Bakhyt Aitzhanova, Leonid Makar-Limanov, Ualbai Umirbaev

The Veronese subalgebra $A_{0}$ of degree $d \geq 2$ of the polynomial algebra $A = K [x_{1}, x_{2}, \dots, x_{n}]$ over a field $K$ in the variables $x_{1}, x_{2}, \dots, x_{n}$ is the subalgebra of $A…

math.RA2023

Representations via differential algebras and equationally Noetherian algebras

Alexander A. Mikhalev, Manat Mustafa, Ualbai Umirbaev

We show that free algebras of the variety of algebras generated by the Witt algebra $W_{n}$ , the left-symmetric Witt algebra $L_{n}$ , and the symplectic Poisson algebra $P_{n}$ can be de…

math.AC2022

Automorphisms of affine Veronese surfaces

Bakhyt Aitzhanova, Ualbai Umirbaev

We prove that every derivation and every locally nilpotent derivation of the subalgebra $K [x^{n}, x^{n - 1} y, \dots, x y^{n - 1}, y^{n}]$ , where $n \geq 2$ , of the polynomial algebra $K [x, y]$ …

math.RA2022★ 13 cited

Polynomial identities in Novikov algebras

Vladimir Dotsenko, Nurlan Ismailov, Ualbai Umirbaev

In this paper, we study Novikov algebras satisfying nontrivial identities. We show that a Novikov algebra over a field of zero characteristic that satisfies a nontrivial identity s…

math.RA2022★ 11 cited

An effective criterion for Nielsen-Schreier varieties

Vladimir Dotsenko, Ualbai Umirbaev

All algebras of a certain type are said to form a Nielsen-Schreier variety if every subalgebra of a free algebra is free. This property has been perceived as extremely rare; in par…

math.RA2021

On the Lie-solvability of Novikov algebras

Kaisar Tulenbaev, Ualbai Umirbaev, Viktor Zhelyabin

We prove that any Novikov algebra over a field of characteristic $\neq = 2$ is Lie-solvable if and only if its commutator ideal $[N, N]$ is right nilpotent. We also construct examples…

math.RA2021

Some examples of nonassociative coalgebras and supercoalgebras

Daniyar Kozybaev, Ualbai Umirbaev, Viktor Zhelyabin

Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan supe…

math.RA2021

Automorphisms of simple quotients of the Poisson and universal enveloping algebras of $sl_{2}$

Altyngul Naurazbekova, Ualbai Umirbaev

Let $P (sl_{2} (K))$ be the Poisson enveloping algebra of the Lie algebra $sl_{2} (K)$ over an algebraically closed field $K$ of characteristic zero. The quotient algebr…

math.RA2021

On the solvability of graded Novikov algebras

Ualbai Umirbaev, Viktor Zhelyabin

We show that the right ideal of a Novikov algebra generated by the square of a right nilpotent subalgebra is nilpotent. We also prove that a $G$ -graded Novikov algebra $N$ over a f…

math.RA2021

Automorphisms of free braided associative algebras in two variables

Riza Mutalip, Altyngul Naurazbekova, Ualbai Umirbaev

We describe the groups of automorphisms of two generated free braided associative algebras with involutive diagonal braidings over a field of characteristic $\neq = 2$ . Depending on…

math.RA2020

A Dixmier theorem for Poisson enveloping algebras

Ualbai Umirbaev, Viktor Zhelyabin

We consider a skew-symmetric $n$ -ary bracket on the polynomial algebra $K [x_{1}, \dots, x_{n}, x_{n + 1}]$ ( $n \geq 2$ ) over a field $K$ of characteristic zero defined by $\{a_1,\ldots,a_n\…

math.RA2020

Differential algebraic dependence and Novikov dependence

Bibinur Duisengalieva, Ualbai Umirbaev

We define an analogue of the Fox derivatives for differential polynomial algebras and give a criterion for differential algebraic dependence of a finite system of elements. In part…

math.RA2020

On the automorphisms of a free Lie algebra of rank 3 over an integral domain

Alibek Alimbaev, Ruslan Nauryzbaev, Ualbai Umirbaev

We prove that the group of tame automorphisms of a free Lie algebra (as well as of a free anticommutative algebra) rank 3 over an arbitrary integral domain has the structure of an…

math.RA2020★ 1 cited

Tame and wild automorphisms of differential polynomial algebras of rank 2

Bibinur Duisengalieva, Altyngul Naurazbekova, Ualbai Umirbaev

It is proved that the tame automorphism group of a differential polynomial algebra $k {x, y}$ over a field $k$ of characteristic $0$ in two variables $x, y$ with $m$ commuting deriv…

math.RA2020

A wild automorphism of a free Novikov algebra

Bibinur Duisengalieva, Ualbai Umirbaev

An example of a non-triangulable locally nilpotent derivation and an example of a wild exponential automorphism of the free Novikov algebra $N ⟨ x, y, z ⟩$ in th…

math.RA2020

The Nagata automorphism of free nonassociative algebras of rank two over Eucledean domains

Alibek Alimbaev, Ualbai Umirbaev

We construct an analogue of the Nagata automorphism of free nonassociative algebras and free commutative algebras of rank two over a Euclidean domain and prove that it is wild.

Automorphisms of Free Metabelian Lie Algebras, II

Chein Automorphisms of Free Metabelian Anticommutative Algebras

Representations of the Grassmann Poisson superalgebras

Tangent Lie Algebras of Automorphism Groups of Free Algebras

Automorphisms and derivations of a universal left-symmetric enveloping algebra

Automorphisms of free metabelian Lie algebras, I

Erroneous proofs of the wildness of some automorphisms of free metabelian Lie algebras

On a variety of right-symmetric algebras

Automorphisms of Veronese subalgebras of polynomial algebras and free Poisson algebras

Representations via differential algebras and equationally Noetherian algebras

Automorphisms of affine Veronese surfaces

Polynomial identities in Novikov algebras

An effective criterion for Nielsen-Schreier varieties

On the Lie-solvability of Novikov algebras

Some examples of nonassociative coalgebras and supercoalgebras

Automorphisms of simple quotients of the Poisson and universal enveloping algebras of sl2​

On the solvability of graded Novikov algebras

Automorphisms of free braided associative algebras in two variables

A Dixmier theorem for Poisson enveloping algebras

Differential algebraic dependence and Novikov dependence

On the automorphisms of a free Lie algebra of rank 3 over an integral domain

Tame and wild automorphisms of differential polynomial algebras of rank 2

A wild automorphism of a free Novikov algebra

The Nagata automorphism of free nonassociative algebras of rank two over Eucledean domains

Automorphisms of simple quotients of the Poisson and universal enveloping algebras of $sl_{2}$