Related papers: The classification of non-characteristically nilpo…

W. A. Moens proved that a Lie algebra is nilpotent if and only if it admits an invertible Leibniz-derivation. In this paper we show that with the definition of Leibniz-derivation from W. A. Moens the similar result for non Lie Leibniz…

We give algebraic and geometric classifications of $4$-dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are $41$ one-parameter families of $4$-dimensional nilpotent terminal (non-Leibniz)…

The paper concerns the classification problem of a subclass of complex filiform Leibniz algebras in dimensions 7 and 8. This subclass arises from naturally graded filiform Lie algebras. We give a complete list of isomorphism classes of…

We give a geometric classification of $n$-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent algebras. We prove that the corresponding geometric varieties are irreducible, find their dimensions and describe explicit…

This paper is devoted to the complete algebraic and geometric classification of complex $5$-dimensional nilpotent binary Leibniz and $4$-dimensional nilpotent mono Leibniz algebras. As a corollary, we have the complete algebraic and…

In this work $n$-dimensional filiform Leibniz algebras admitting a gradation of length $(n-1)$ are classified. Derivations of such algebras are also described.

We classify all nonnilpotent, solvable Leibniz algebras with the property that all proper subalgebras are nilpotent. This generalizes the work of Stitzinger and Towers in Lie algebras. We show several examples which illustrate the…

In this paper we present the classification of a subclass of naturally graded Leibniz algebras. These $n$-dimensional Leibniz algebras have the characteristic sequence equal to (n-3,3). For this purpose we use the software Mathematica.

In general, the study of gradations has always represented a cornerstone in algebra theory. In particular, \textit{naturally graded} seems to be the first and the most relevant gradation when it comes to nilpotent algebras, a large class of…

This paper deals with the classification of Leibniz central extensions of a naturally graded filiform Lie algebra. We choose a basis with respect to that the table of multiplication has a simple form. In low dimensional cases isomorphism…

The Leibniz algebras appear as a generalization of the Lie algebras \cite{loday}. The classification of naturally graded $p$-filiform Lie algebras is known \cite{C-G-JM}, \cite{J.Lie.Theory}, \cite{AJM}, \cite{Ve}. In this work we deal with…

Leibniz superalgebras with nilindex $n + m$ and characteristic sequence $(n-1, 1 \ | \ m)$ divided into four parametric classes that contain a set of non-isomorphic superalgebras. In this paper, we give a complete classification of solvable…

The aim of this work is to present the description up to isomorphism of Leibniz superalgebras with characteristic sequence (n | m-1, 1) and nilindex n+m.

In this paper we study the Lie algebras of derivations of two-step nilpotent algebras. We obtain a class of Lie algebras with trivial center and abelian ideal of inner derivations. Among these, the relations between the complex and the real…

The description of complex solvable Leibniz algebras whose nilradical is a naturally graded filiform algebra is already known. Unfortunately, a mistake was made in that description. Namely, in the case where the dimension of the solvable…

In this paper we study non-nilpotent non-Lie Leibniz $\mathbb{F}$-algebras with one-dimensional derived subalgebra, where $\mathbb{F}$ is a field with $\operatorname{char}(\mathbb{F}) \neq 2$. We prove that such an algebra is isomorphic to…

This paper is devoted to the complete algebraic and geometric classification of complex $5$-dimensional nilpotent Leibniz algebras. In particular, the variety of complex $5$-dimensional nilpotent Leibniz algebras has dimension $24$ it has…

For each 3-dimensional non-Lie Leibniz algebra over the complex numbers, we describe the algebra of polynomial invariants and determine its group of automorphisms. As a consequence, we establish that any two non-nilpotent 3-dimensional…

The article presents the structure of the automorphism groups of two types of non-nilpotent Leibniz algebras with a dimension of 3.

We extend the classification of solvable Lie algebras with abelian nilradicals to classify solvable Leibniz algebras which are one dimensional extensions of an abelian nilradicals.