On Classification of Filiform Leibniz Algebras

Abstract

In this work we prove that in classifying of filiform Leibniz algebras whose naturally graded algebra is a non-Lie algebra, it suffices to consider some special basis transformations. Moreover, we derive a criterion for two such Leibniz algebras to be isomorphic in terms of such transformations. The classification problem of filiform Leibniz algebras whose naturally graded algebra is non-Lie in an arbitrary dimension, is reduced to the investigation of the conditions obtained.