U. Umirbaev

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20202025

most citedTame and wild automorphisms of differential polynomial algebras of rank 2

1 citations · 1 across the 12 of their papers we have counts for

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17 papers · 1 filter

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.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.