Classification of solvable Leibniz algebras with null-filiform nilradical

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...

Solvable Lie algebras with $N(R_n,m,r)$ nilradical

In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.

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...

On the filiform Leibniz algebras of maximal length

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...