S. A. Sheraliyeva | Searcharxiv

arXiv2025

Abelian extensions of five-dimensional solvable Leibniz algebras

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-dimensional solvable Leibniz algebras with a non-trivial three-dimensional nilradical is obtained. Furthermore, we explore extensions of solvable Leibniz algebras whose nilradical is null-filiform, establishing that, in this case, there exists a unique solvable abelian extension.

math.RA↗

arXiv2022

Extensions of solvable Lie algebras with naturally graded filiform nilradical

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 $n_{n, 1}$ and $Q_{2n}.$ We find all one-dimensional central extensions of the algebra $n_{n, 1}$ and show that any extension of $Q_{2n}$ is split. After that we find one-dimensional extensions of solvable Lie algebras with nilradical $n_{n, 1}$. We prove that there exists a unique non-split central extension of solvable Lie algebras with nilradical $n_{n, 1}$ of maximal codimension. Moreover, all one-dimensional extensions of solvable Lie algebras with nilradical $n_{n, 1}$ whose codimension is equal to one are found and compared these solvable algebras with the solvable algebras with nilradicals are one-dimensional central extension of algebra $n_{n, 1}$.

math.RA↗