arXiv subjects

Azamat Saydaliyev

Publications and source records attributed to Azamat Saydaliyev.

4 recordsLinked to original sources

arXiv2026

The geometric classification of left-symmetric algebras and superalgebras

We investigate the geometric classification of complex left-symmetric algebras and left-symmetric superalgebras in low dimensions. Building on the algebraic classifications of Bai and Zhang for 3-dimensional left-symmetric algebras and for 2- and 3-dimensional left-symmetric superalgebras, we determine all degenerations and non-degenerations among their isomorphism classes. We prove that the variety of 3-dimensional left-symmetric algebras has dimension 10 and decomposes into 31 irreducible components, ten of which are rigid. For left-symmetric superalgebras, we describe the irreducible components, determine their dimensions, and identify the rigid superalgebras in the varieties of dimensions (1,1), (1,2), and (2,1).

math.RA↗

arXiv2025

The complete classification of irreducible components of varieties of Jordan superalgebras

The aim of the present short note is to answer the open questions posted by Hern\'andez, Martin, and Rodrigues in {\rm \cite{p1,p2}}. The obtained results give the complete classification of irreducible components in the varieties of Jordan superalgebras of types $(3,1)$ and $(2,2).$

math.RA↗

arXiv2025

The algebraic and geometric classification of Jordan superalgebras

We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.

math.RA↗

arXiv2024

Transposed Poisson structures on quasi-filiform Lie algebras of maximum length

This article will discussing on $\frac{1}{2}$-derivations of quasi-filiform Lie algebras of maximum length. The non-trivial transposed Poisson algebras with the quasi-filiform Lie algebras of maximum length are constructed by using $\frac{1}{2}$-derivations of Lie algebras. We have established commutative associative multiplication to construct a transposed Poisson algebra with an associated given Lie algebra.

math.RA↗