On classification of complex filiform Leibniz algebras

TL;DR

This paper develops a method to classify complex filiform Leibniz algebras with non-Lie naturally graded algebras by using special basis transformations and provides criteria for algebra isomorphism.

Contribution

It introduces a simplified classification approach for these algebras and establishes isomorphism criteria based on basis transformations.

Findings

Classification reduces to analyzing special basis transformations.

Provides explicit criteria for algebra isomorphism.

Simplifies the classification process in arbitrary dimensions.

Abstract

In this paper we prove that in classifying of complex filiform Leibniz algebras, for which its naturally graded algebra is non-Lie algebra, it suffices to consider some special basis transformations. Moreover, we establish a criterion whether given two such Leibniz algebras are isomorphic in terms of such transformations. The classification problem of filiform Leibniz algebras, for which its naturally graded algebras are non-Lie in an arbitrary dimension, is reduced to the investigation of the obtained conditions.