Classification of nilpotent Lie algebras of nilpotency class 3 having a derived subalgebra of dimension three

TL;DR

This paper provides a complete classification of certain nilpotent Lie algebras of class 3 with specific derived subalgebra dimensions, including explicit structures for seven-dimensional cases.

Contribution

It offers a comprehensive classification of nilpotent Lie algebras with nilpotency class 3, derived subalgebra dimension 3, and explicit structures for dimension 7.

Findings

Classification of nilpotent Lie algebras with specified properties

Explicit structure descriptions for 7-dimensional cases

Complete characterization of these Lie algebras

Abstract

In this paper, we investigate nilpotent Lie algebras $ L $ of nilpotency class $3 $ and provide a complete classification of those satisfying $ \dim L^2 = 3 $ and $Z(L) = L^3 \cong A(2). $ Furthermore, we explicitly characterize the structure of such Lie algebras in the case when $ \dim L = 7. $