arXiv subjects

Maqpal Eraliyeva

Publications and source records attributed to Maqpal Eraliyeva.

3 recordsLinked to original sources

arXiv2026

Classification of $3$-dimensional unital commutative algebras

We present the complete classification of non-isomorphic complex $3$-dimensional unital commutative algebras. Every such algebra decomposes canonically as $\mathbb Ce_1\oplus V$, where $e_1$ is the unit and $V$ is the kernel of the trace form; the induced traceless $2$-dimensional commutative algebra on $V$ is one of four algebras, and the classification reduces to the classification of symmetric bilinear forms on $V$ up to the automorphisms of this kernel. The answer consists of six algebras, three one-parameter families, one two-parameter family and one three-parameter family.

math.RA↗

arXiv2026

Unital $3$-dimensional structurable algebras: classification, properties and $\rm{AK}$-construction

This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras for type $(1, 2).$ For each obtained algebra, we describe the derivation algebra, the automorphism group, the lattice of subalgebras and ideals, and functional identities of degree $2$. Furthermore, we investigate the Allison-Kantor construction for the classified algebras. We determine the structure of the resulting $\mathbb{Z}$-graded Lie algebras, providing their dimensions and Levi decompositions.

math.RA↗

arXiv2025

Transposed $δ$-Poisson algebra structures on null-filiform associative algebras

In this paper, we consider transposed $δ$-Poisson algebras, which are a generalization of transposed $δ$-Poisson algebras. In particular, we describe all transposed $δ$-Poisson algebras of associative null-filiform algebras. It can be seen that these algebras are characterized by the roots of the polynomial $δ^3 - 3δ^2 + 2δ$. A complete classification of transposed $δ$-Poisson algebras corresponding to each value of the parameter $δ$ is provided. Furthermore, we construct all $δ$-Poisson algebra structures on null-filiform associative algebras, and show that they are trivial $δ$-Poisson algebras.

math.RA↗