Related papers: Leibniz superalgebras and central extensions
In this note we point out that the definition of the universal enveloping dialgebra for a Leibniz algebra is consistent with the interpretation of a Leibniz algebra as a generalization not of a Lie algebra, but of the adjoint representation…
The aim of this work is to present the first problems that appear in the study of nilpotent Leibniz superalgebras. These superalgebras and so the problems, will be considered as a natural generalization of nilpotent Leibniz algebras and Lie…
Basing ourselves on Janelidze and Kelly's general notion of central extension, we study universal central extensions in the context of semi-abelian categories. Thus we unify classical, recent and new results in one conceptual framework. The…
Leibniz algebras are certain generalizations of Lie algebras. Motivated by the concept of subinvariance in group theory, Schenkman studied properties of subinvariant subalgebras of a Lie algebra. In this paper we define subinvariant…
In this paper, we introduce the notion Lie-derivation. This concept generalizes derivations for non-Lie Leibniz algebras. We study these Lie-derivations in the case where their image is contained in the Lie-center, call them Lie-central…
This paper concerns the study of Leibniz algebras, a natural generalization of Lie algebras, from the perspective of centralizers of elements. We study conditions on Leibniz algebras under which centralizers of all elements are ideals. We…
The goal of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $\mathfrak{g} \otimes \mathbb{C}[t,t^{-1},u]$ with finite dimensional simple Lie…
We extend results related to maximal subalgebras and ideals from Lie to Leibniz algebras. In particular, we classify minimal non-elementary Leibniz algebras and Leibniz algebras with a unique maximal ideal. In both cases, there are types of…
In this paper, we consider Leibniz algebras with derivations. A pair consisting of a Leibniz algebra and a distinguished derivation is called a LeibDer pair. We define a cohomology theory for LeibDer pair with coefficients in a…
If one wishes to define a complete Leibniz algebra in such a way as to extend the notion of a complete Lie algebra, two distinct definitions can be found in the current literature. Since biderivations on complete Lie algebras have already…
In this paper we study the notion of isoclinism on Lie-central extensions of Leibniz algebras, this yields to introduce the concept of Lie-isoclinic Leibniz algebras. We provide several equivalent conditions under which Leibniz algebras are…
In this paper, first we classify non-abelian extensions of Leibniz algebras by the second non-abelian cohomology. Then, we construct Leibniz 2-algebras using derivations of Leibniz algebras, and show that under a condition on the center, a…
Leibniz algebras ${\mathcal E}_n$ were introduced as algebraic structure underlying U-duality. Algebras ${\mathcal E}_3$ derived from Bianchi three-dimensional Lie algebras are classified here. Two types of algebras are obtained:…
We study the central extensions of Lie algebras graded by an irreducible locally finite root system.
The purpose of this article is to show a close relationship between the generalized central series of Leibniz algebras. Some analogues of the classical group-theoretical theorems of Schur and Baer for Leibniz algebras are proved.
In this work we study Leibniz algebras whose second-maximal subalgebras are ideals. We provide a classification based on solvability, nilpotency, and the size of the derived algebra. We give specific descriptions of those Leibniz algebras…
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.
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…
A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form will be called a NIS-Lie (super)algebra. The double extension of a NIS-Lie (super)algebra is the result of simultaneously adding to it a central element and an…
In this paper we begin to study the subalgebra lattice of a Leibniz algebra. In particular, we deal with Leibniz algebras whose subalgebra lattice is modular, upper semi-modular, lower semi-modular, distributive, or dually atomistic. The…