On Filiform and 2-Filiform Leibniz Algebras of Maximum Length

Abstract

Leibniz algebras appear as a generalization of Lie algebras. The classification of naturally graded p-filiform Lie algebras is known. Several authors have studied the naturally graded p-filiform Leibniz algebras for any p with p > 0. G´omez, Jim´enez-Merch´an and Reyes have investigated families of nilpotent Lie algebras with other types of non-natural gradation, a gradation with a large number of subspaces. The algebras with maximum number of subspaces in the gradation will be called maximum length algebras. In this work we deal with the classification of filiform and 2-filiform Leibniz algebras of maximum length.