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

Saboura Yousefi; Azam Kaheni; Farangis Johari

paper

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

arXiv:2511.18941

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 $Z (L) = L^{3} ≅ A (2) .$ Furthermore, we explicitly characterize the structure of such Lie algebras in the case when $dim L = 7.$