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Jobir Adashev

Publications and source records attributed to Jobir Adashev.

6 recordsLinked to original sources
arXiv2026

$\delta$-Leibniz algebras and related $\delta$-type algebras

This paper introduces and investigates the structure of $\delta$-Leibniz algebras, which serve as a parametric generalization of classical Leibniz algebras defined by a scalar $\delta$. The authors define $\delta$-Lie algebras, $\delta$-Lie dialgebras, and $\delta$-Zinbiel algebras via a standard procedure and study their fundamental properties. Furthermore, the research describes symmetric $\delta$-Leibniz algebras and algebras of $\delta$-biderivation type, establishing their connections with nilalgebras. Finally, these results provide a unified framework for understanding various classes of non-associative algebras through the lens of the $\delta$ parameter.

math.RA↗
arXiv2024

Classification of four-dimensional anti-dendriform algebras whose associated associative algebra has the center of dimension one

This article is devoted to the classification of anti-dendriform algebras that are associated with associativity. They are characterized as algebras with two operations whose sum is associative. In the paper all four-dimensional complex anti-dendriform algebras associated to four-dimensional associative algebras with one-dimensional center are classified

math.RA↗
arXiv2024

Transposed Poisson structures on solvable Lie algebras with filiform nilradical

In this article, we described 1/2-derivations of solvable Lie algebras with a thread-like nilradical. Nontrivial transposed Poisson algebras with solvable Lie algebras are constructed. That is, by using 1/2-derivations of Lie algebras, we have established commutative associative multiplication to construct a transposed Poisson algebra with an associated given Lie algebra.

math.RA↗
arXiv2021

The algebraic and geometric classification of nilpotent left-symmetric algebras

This paper is devoted to the complete algebraic and geometric classification of complex $4$-dimensional nilpotent left-symmetric algebras. The corresponding geometric variety has dimension $15$ and decomposes into $3$ irreducible components determined by the Zariski closures of two one-parameter families of algebras and a two-parameter family of algebras (see Theorem B). In particular, there are no rigid $4$-dimensional complex nilpotent left symmetric algebras.

math.RA↗