# Filiform Lie algebras with low derived length

## TL;DR

This paper constructs specific examples of complex filiform Lie algebras with low derived length for any dimension n ≥ 5, and also provides examples with higher derived length, advancing understanding of their structural properties.

## Contribution

It introduces a method to construct n-dimensional filiform Lie algebras with derived length at most 3 and presents examples with greater derived length, expanding the classification.

## Key findings

- Existence of n-dimensional filiform Lie algebras with derived length ≤ 3 for all n ≥ 5
- Examples of filiform Lie algebras with derived length > 3
- Construction techniques for these Lie algebras

## Abstract

We construct, for any integer n greater than or equal to 5, a family of complex filiform Lie algebras with derived length at most 3 and dimension n. We also give examples of n-dimensional filiform Lie algebras with derived length greater than 3.