Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras

Naturally graded quasi-filiform Leibniz algebras

The classification of naturally graded quasi-filiform Lie algebras is known; they have the characteristic sequence (n − 2, 1, 1) where n is the dimension of the algebra. In the present paper we deal with naturally graded quasi-filiform non-Lie–Leibniz algebras which are described by the characteristic sequence C(L) = (n − 2, 1, 1) or C(L) = (n − 2, 2). The first case has been studied in [Camach...

On Low-Dimensional Filiform Leibniz Algebras and Their Invariants

The paper deals with the complete classification of a subclass of complex filiform Leibniz algebras in dimensions 5 and 6. This subclass arises from the naturally graded filiform Lie algebras. We give a complete list of algebras. In parametric families cases, the corresponding orbit functions (invariants) are given. In discrete orbits case, we show a representative of the orbits. 2010 Mathemati...

On the filiform Leibniz algebras of maximal length

On Derivations of Some Classes of Leibniz Algebras

In this paper, we describe the derivations of complex n-dimensional naturally graded filiform Leibniz algebras NGF1, NGF2, and NGF3. We show that the dimension of the derivation algebras of NGF1 and NGF2 equals n+1 and n+2, respectively, while the dimension of the derivation algebra of NGF3 is equal to 2n−1. The second part of the paper deals with the description of the derivations of complex n...

On Classification of Complex Filiform Leibniz

Abstract. This work deal with Leibniz algebras. It is shown that in classifying of filiform non-Lie Leibniz algebras over the field of complex numbers which are obtained from the naturally graded non-Lie Leibniz algebras it suffices to consider some special basis transformations. Using this result, we derive a criterion that ascertains whether given two such filiform non-Lie Leibniz algebras ar...