U. Umirbaev

collaborators

5 papers

math.RA2026

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.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…