arXiv subjects

Nigora Daukeyeva

Publications and source records attributed to Nigora Daukeyeva.

2 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

Transposed $\delta$-Poisson algebra structures on null-filiform associative algebras

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

math.RA↗