A. Khudoyberdiyev

activity

20062025

most citedThe algebraic and geometric classification of nilpotent Novikov algebras

43 citations · 141 across the 44 of their papers we have counts for

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45 papers · 1 filter

math.RA2025

Lie affgebra structures on three-dimensional solvable Lie algebras

Kh. R. Berdalova, A. Kh. Khudoyberdiyev

In this work, the complex Lie affgebra structures on three-dimensional solvable Lie algebras are completely determined.

math.RA2025

Abelian extensions of five-dimensional solvable Leibniz algebras

A. Kh. Khudoyberdiyev, S. A. Sheraliyeva

In this work, we extend the central extension method for solvable Leibniz algebras. Using this method, a complete classification of one-dimensional abelian extensions of five-dimen…

math.RA2025★ 1 cited

The geometric classification of nilpotent Lie-Yamaguti, Bol and compatible Lie algebras

Kobiljon Abdurasulov, Abror Khudoyberdiyev, Feruza Toshtemirova

The geometric classifications of complex $4$ -dimensional nilpotent Lie-Yamaguti algebras, $4$ -dimensional nilpotent Bol algebras, and $4$ -dimensional nilpotent compatible Lie algeb…

math.RA2024

Transposed Poisson structures on Virasoro-type algebras

Ivan Kaygorodov, Abror Khudoyberdiyev, Zarina Shermatova

We compute $\frac{1}{2}$ -derivations on the deformed generalized Heisenberg-Virasoro algebras and on not-finitely graded Heisenberg-Virasoro algebras $W_{n} (G)$ , $\widetild…

math.RA2024

The algebraic classification of nilpotent bicommutative algebras

Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev

This paper is devoted to the complete algebraic classification of complex 5-dimensional nilpotent bicommutative algebras.

math.RA2024

Transposed Poisson structures on Witt-type algebras

Ivan Kaygorodov, Abror Khudoyberdiyev, Zarina Shermatova

We compute $\frac{1}{2}$ -derivations on the deformative Schrödinger-Witt algebra, on not-finitely graded Witt algebras $W_{n} (G)$ , and on not-finitely graded Heisenberg-Witt algebra…

math.RA2024

Local derivations and automorphisms of nilpotent Lie algebra

Abror Khudoyberdiyev, Doston Jumaniyozov

The paper is devoted to the study of local derivations and automorphisms of nilpotent Lie algebras. Namely, we proved that nilpotent Lie algebras with indices of nilpotency $3$ and…

math.RA2024

Local and 2-local $\frac{1}{2}$ -derivations on finite-dimensional Lie algebras

Abror Khudoyberdiyev, Bakhtiyor Yusupov

In this work, we introduce the notion of local and $2$ -local $δ$ -derivations and describe local and $2$ -local $\frac{1}{2}$ -derivation of finite-dimensional solvable Lie algebras w…

math.RA2024★ 3 cited

The algebraic classification of nilpotent Novikov algebras

Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev

This paper is devoted to the complete algebraic classification of complex $5$ -dimensional nilpotent Novikov algebras.

math.RA2023★ 7 cited

Transposed Poisson structures on solvable and perfect Lie algebras

Ivan Kaygorodov, Abror Khudoyberdiyev

We described all transposed Poisson algebra structures on oscillator Lie algebras, i.e., on one-dimensional solvable extensions of the $(2 n + 1)$ -dimensional Heisenberg algebra; on s…

math.RA2023

The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras

Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev

This paper is devoted to the complete algebraic and geometric classification of complex $5$ -dimensional nilpotent binary Leibniz and $4$ -dimensional nilpotent mono Leibniz algebras…

math.RA2023

The algebraic and geometric classification of nilpotent Leibniz algebras

Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev

This paper is devoted to the complete algebraic and geometric classification of complex $5$ -dimensional nilpotent Leibniz algebras. In particular, the variety of complex $5$ -dimens…

math.RA2023★ 1 cited

Transposed Poisson structures on Schrodinger algebra in (n+1)-dimensional space-time

Yang Yang, Xiaomin Tang, Abror Khudoyberdiyev

Transposed Poisson structures on the Schrödinger algebra in $(n + 1)$ -dimensional space-time of Schrödinger Lie groups are described. It was proven that the Schrödinger algebra $\mat…

math.RA2023★ 1 cited

Classification of five-dimensional symmetric Leibniz algebras

Iroda Choriyeva, Abror Khudoyberdiyev

In this paper we give the complete classification of $5$ -dimensional complex solvable symmetric Leibniz algebras.

math.RA2022

Extensions of solvable Lie algebras with naturally graded filiform nilradical

A. Kh. Khudoyberdiyev, S. A. Sheraliyeva

In this work we consider extensions of solvable Lie algebras with naturally graded filiform nilradicals. Note that there exist two naturally graded filiform Lie algebras $n_{n, 1}$ …

math.RA2021★ 2 cited

The algebraic classification of nilpotent commutative algebras

Doston Jumaniyozov, Ivan Kaygorodov, Abror Khudoyberdiyev

This paper is devoted to the complete algebraic classification of complex $5$ -dimensional nilpotent commutative algebras. Our method of classification is based on the standard meth…

math.RA2021★ 1 cited

The geometric classification of nilpotent commutative $CD$ -algebras

Doston Jumaniyozov, Ivan Kaygorodov, Abror Khudoyberdiyev

We give a geometric classification of complex $5$ -dimensional nilpotent commutative $CD$ -algebras. The corresponding geometric variety has dimension $24$ and decomposes…

math.RA2021★ 3 cited

The algebraic classification of nilpotent commutative $CD$ -algebras

Doston Jumaniyozov, Ivan Kaygorodov, Abror Khudoyberdiyev

An algebraic classification of complex $5$ -dimensional nilpotent commutative $CD$ -algebras is given. This classification is based on an algebraic classification of compl…

math.RA2021★ 5 cited

The algebraic and geometric classification of nilpotent left-symmetric algebras

Jobir Adashev, Ivan Kaygorodov, Abror Khudoyberdiyev +1

This paper is devoted to the complete algebraic and geometric classification of complex $4$ -dimensional nilpotent left-symmetric algebras. The corresponding geometric variety has d…

math.RA2020★ 9 cited

Central extensions of filiform Zinbiel algebras

Luisa M. Camacho, Iqboljon Karimjanov, Ivan Kaygorodov +1

In this paper we describe central extensions (up to isomorphism) of all complex null-filiform and filiform Zinbiel algebras. It is proven that every non-split central extension of…

math.RA2020★ 6 cited

One-generated nilpotent terminal algebras

Ivan Kaygorodov, Abror Khudoyberdiyev, Aloberdi Sattarov

We give an algebraic classification of complex $5$ -dimensional one-generated nilpotent terminal algebras.

math.RA2020★ 7 cited

One-generated nilpotent Novikov algebras

Luisa M. Camacho, Iqboljon Karimjanov, Ivan Kaygorodov +1

We give a classification of 5- and 6-dimensional complex one-generated nilpotent Novikov algebras

math.RA2019★ 18 cited

The algebraic and geometric classification of nilpotent noncommutative Jordan algebras

Doston Jumaniyozov, Ivan Kaygorodov, Abror Khudoyberdiyev

We give algebraic and geometric classifications of complex $4$ -dimensional nilpotent noncommutative Jordan algebras. Specifically, we find that, up to isomorphism, there are only $…

math.RA2019★ 1 cited

Local and 2-local derivations of solvable Leibniz algebras

Sh. A. Ayupov, A. Kh. Khudoyberdiyev, B. B. Yusupov

We show that any local derivation on the solvable Leibniz algebras with model or abelian nilradicals, whose the dimension of complementary space is maximal is a derivation. We show…

Lie affgebra structures on three-dimensional solvable Lie algebras

Abelian extensions of five-dimensional solvable Leibniz algebras

The geometric classification of nilpotent Lie-Yamaguti, Bol and compatible Lie algebras

Transposed Poisson structures on Virasoro-type algebras

The algebraic classification of nilpotent bicommutative algebras

Transposed Poisson structures on Witt-type algebras

Local derivations and automorphisms of nilpotent Lie algebra

Local and 2-local 21​-derivations on finite-dimensional Lie algebras

The algebraic classification of nilpotent Novikov algebras

Transposed Poisson structures on solvable and perfect Lie algebras

The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras

The algebraic and geometric classification of nilpotent Leibniz algebras

Transposed Poisson structures on Schrodinger algebra in (n+1)-dimensional space-time

Classification of five-dimensional symmetric Leibniz algebras

Extensions of solvable Lie algebras with naturally graded filiform nilradical

The algebraic classification of nilpotent commutative algebras

The geometric classification of nilpotent commutative CD-algebras

The algebraic classification of nilpotent commutative CD-algebras

The algebraic and geometric classification of nilpotent left-symmetric algebras

Central extensions of filiform Zinbiel algebras

One-generated nilpotent terminal algebras

One-generated nilpotent Novikov algebras

The algebraic and geometric classification of nilpotent noncommutative Jordan algebras

Local and 2-local derivations of solvable Leibniz algebras

Local and 2-local $\frac{1}{2}$ -derivations on finite-dimensional Lie algebras

The geometric classification of nilpotent commutative $CD$ -algebras

The algebraic classification of nilpotent commutative $CD$ -algebras