Capability of Nilpotent Lie Algebras of Small Dimension

On characterizing nilpotent Lie algebras by their multiplier, $$s(L)=4$$

“…Let L be a Lie algebra and Z(L) ⊆ L 2 . By using[20, Theorem 1.1] and looking at the classification of all nilpotent Lie algebras in[9], L 6,10 , 27A and 157 are non-capable Lie algebras with derived subalgebra of dimension 2. Since Z(L) ⊆ L 2 , L is isomorphic to one of the nilpotent Lie algebras L Lie algebra and Z(L) ⊆ L 2 .…”