Related papers: Some cohomologically rigid solvable Leibniz algebr…
From the viewpoint of semi-abelian homology, some recent results on homology of Leibniz n-algebras can be explained categorically. In parallel with these results, we develop an analogous theory for Lie n-algebras. We also consider the…
In this paper, an explicit construction of a countable parafree Lie algebra over $\mathbb Z/2$ with nonzero second homology is given. It is also shown that the cohomological dimension of the pronilpotent completion of a free noncyclic…
In this paper, we find a family $SL^{n,m}$, in any arbitrary dimensions, of cohomologically rigid solvable Lie superalgebras with nilradical the model filiform Lie superalgebra $L^{n,m}$. Moreover, we exhibit a family of cohomologically…
The concept of breadth has been used in the classification of p-groups and nilpotent Lie algebras. In this paper, we investigate this notion for finite-dimensional solvable Lie algebras. Our main focus is to characterize solvable Lie…
Solvable Lie algebras having at least one Abelian descending central ideal are studied. It is shown that all such Lie algebras can be built up from canonically defined ideals. The nature of such ideals is elucidated and their construction…
Bakalov, Kac and Voronov introduced Leibniz conformal algebras (and their cohomology) as a non-commutative analogue of Lie conformal algebras. Leibniz conformal algebras are closely related to field algebras which are non-skew-symmetric…
A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of…
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…
The goal of this paper is to describe the structure of finite-dimensional semi-simple Leibniz algebras in characteristic zero. Our main tool in this endeavor are hemi-semidirect products. One of the major results of this paper is a…
We investigate Lie algebras whose Lie bracket is also an associative or cubic associative multiplication to characterize the class of nilpotent Lie algebras with a nilindex equal to 2 or 3. In particular we study the class of 2-step…
An infinite filiform Lie algebra L is residually nilpotent and its graded associated with respect to the lower central series has smallest possible dimension in each degree but is still infinite. This means that gr(L) is of dimension two in…
In this paper, we study a class of Leibniz conformal algebras called quadratic Leibniz conformal algebras. An equivalent characterization of a Leibniz conformal algebra $R=\mathbb{C}[\partial]V$ through three algebraic operations on $V$ are…
The space of Lie algebra cohomology is usually described by the dimensions of components of certain degree even for the adjoint module as coefficients when the spaces of cochains and cohomology can be endowed with a Lie superalgebra…
Associative conformal algebras of conformal endomorphisms are of essential importance for the study of finite representations of conformal Lie algebras (Lie vertex algebras). We describe all semisimple algebras of conformal endomorphisms…
We construct a cochain map embedding the cohomology complex of any dual Leibniz algebra $B$ into the Lie algebra cochain complex of $\mathfrak{g} \otimes B$, where $\mathfrak{g}$ is a Leibniz algebra. This reduces the study of dual Leibniz…
We present a constructive approach to torsion-free gradings of Lie algebras. Our main result is the computation of a maximal grading. Given a Lie algebra, using its maximal grading we enumerate all of its torsion-free gradings as well as…
We study sympathetic Lie algebras, namely perfect and complete Lie algebras. They arise among other things in the study of adjoint Lie algebra cohomology. This is motivated by a conjecture of Pirashvili, which says that a non-trivial…
We construct homology with trivial coefficients of Hom-Leibniz $n$-algebras. We introduce and characterize universal ($\alpha$)-central extensions of Hom-Leibniz $n$-algebras. In particular, we show their interplay with the zeroth and first…
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.
We give a necessary and sufficient criterion for the solvability of $\operatorname{HH}^1(kP)$ as a Lie algebra, where $P$ is a $p$-group with $p$ odd, in terms of a directed graph constructed from the group $P$. This gives non-trivial…