Related papers: k-Step Nilpotent Lie Algebras
A finite dimensional filiform K-Lie algebra is a nilpotent Lie algebra g whose nil index is maximal, that is equal to dim g -1. We describe necessary and sufficient conditions for a filiform algebra over an algebraically closed field of…
We present a construction of 2-step nilpotent Lie algebras using labeled directed simple graphs, which allows us to give a criterion to detect certain ideals and subalgebras by finding special subgraphs. We prove that if a label occurs only…
We construct, for any integer n greater than or equal to 5, a family of complex filiform Lie algebras with derived length at most 3 and dimension n. We also give examples of n-dimensional filiform Lie algebras with derived length greater…
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…
Every symplectic Lie algebra with degenerate (including non-abelian nilpotent symplectic Lie algebras) has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding…
This paper studies how many orthogonal bi-invariant complex structures exist on a metric Lie algebra over the real numbers. Recently, it was shown that irreducible Lie algebras which are additionally $2$-step nilpotent admit at most one…
The Leibniz algebras appeared as a generalization of the Lie algebras. In this work we deal with the classification of nilpotent complex Leibniz algebras of low dimensions. Namely, the classification of nilpotent complex Leibniz algebras…
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…
We study symplectic (contact) structures on nilmanifolds that correspond to the filiform Lie algebras - nilpotent Lie algebras of the maximal length of the descending central sequence. We give a complete classification of filiform Lie…
The purpose of this paper is to classify all $p$-nilpotent restricted Lie algebras of dimension 5 over perfect fields of characteristic $p\geq 5$. Our work builds upon the recent work of Schneider and Usefi on the classification of…
We present the classification of real nilpotent quasi-filiform Lie algebras endowed with a complex structure. A nilpotent Lie algebra g is called quasi-filiform is the nilindex is equal to dim(n)-2. We recall that the filiform case…
We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence of a half-flat SU(3)-structure. We obtain a classification of the 6-dimensional…
We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over R and C, as well as the classification of the 4-dimensional…
Given a nilpotent Lie algebra $\mathfrak n$ we construct a spectral sequence which is derived from a filtration of its Chevalley-Eilenberg differential complex and converges to the Lie algebra cohomology of $\mathfrak n$. The limit of this…
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…
We study nilpotent Lie algebras endowed with a complex structure and a quadratic structure which is pseudo-Hermitian for the given complex structure. We propose several methods to construct such Lie algebras and describe a method of double…
In this paper we classify filiform associative algebras of degree $k$ over a field of characteristic zero. Moreover, we also classify naturally graded complex filiform and quasi-filiform nilpotent associative algebras which are described by…
In this paper we obtain the classification of $p$-nilpotent restricted Lie algebras of dimension at most four over a perfect field of characteristic p.
We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint…
The filiform and the quasi-filiform Lie algebras form a special class of nilpotent Lie algebras. The aim of this paper is to compute the index and provide regular vectors of this two class of nilpotent Lie algebras. we consider the graded…