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

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