Related papers: On some solvable Leibniz algebras and their comple…
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…
We construct all solvable Lie algebras with a specific n-dimensional nilradical n_{n,3} which contains the previously studied filiform nilpotent algebra n_{n-2,1} as a subalgebra but not as an ideal. Rather surprisingly it turns out that…
This thesis was concerned with classifying the real indecomposable solvable Lie algebras with codimension one nilradicals of dimensions two through seven. This thesis was organized into three chapters. In the first, we described the…
This paper is a contribution to the development of the non associative algebras theory. More precisely, this work deals with the classification of the complex 4-dimensional Leibniz algebras. Note that the classification of 4-dimensional…
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 is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the variety of Leibniz algebras. It is shown that, up to isomorphism, there exist three…
This work completes the study of the solvable Leibniz algebras, more precisely, it completes the classification of the $3$-filiform Leibniz algebras of maximum length \cite{3-filiform}. Moreover, due to the good structure of the algebras of…
Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived…
For a sequence of the naturally graded quasi-filiform Leibniz algebra of second type $\mathcal{L}^2$ introduced by Camacho, G\'{o}mez, Gonz\'{a}lez and Omirov, all possible right and left solvable indecomposable extensions over the field…
In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by…
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…
This paper is concerned with generalising the results for Lie $CT$-algebras to Leibniz algebras. In some cases our results give a generalisation even for the case of a Lie algebra. Results on $A$-algebras are used to show every Leibniz…
The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…
We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to…
In this paper we describe the infinitesimal deformations of null-filiform Leibniz superalgebras over a field of zero characteristic. It is known that up to isomorphism in each dimension there exist two such superalgebras $NF^{n,m}$. One of…
In this paper, we provide a complete description of complex maximal solvable extensions for a certain class of nilpotent Lie algebras. In particular, we show that, up to isomorphism, a solvable extension of a $d$-locally diagonalizable…
In this paper, we are interested in solvable complete Lie algebras, over the field $\K=\R$ or $\mathbb{C}$, which admit a symplectic structure. Specifically, important classes are studied, and a description of complete Lie Algebra with the…
In this paper we investigate the derivations of filiform Leibniz algebras. Recall that the set of filiform Leibniz algebras of fixed dimension is decomposed into three non-intersected families. We found sufficient conditions under which…
Leibniz algebras are certain generalization of Lie algebras. In this paper we give the classification of four dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear…
In this paper we introduce the notion of pure non-characteristically nilpotent Lie algebra and under a condition we prove that a complex maximal extension of a finite-dimensional pure non-characteristically nilpotent Lie algebra is…