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

Abstract

In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly nilpotent.

The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras

“…A systematic study of algebraic properties of Leibniz algebras is started from the Loday paper. So, several classical theorems from Lie algebras theory have been extended to the Leibniz algebras case; many classification results regarding nilpotent, solvable, simple, and semisimple Leibniz algebras are obtained (see, for example, [4,7,14,32,33,40,44,47,50] and references therein). Leibniz algebras is a particular case of terminal algebras and, on the other hand, symmetric Leibniz algebras are Poisson admissible algebras.…”