Solvable Leibniz Algebras with 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 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...

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.