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

Abstract

Let L be a non-abelian nilpotent Lie algebra of dimension n and $$s(L)=\frac{1}{2}(n-1)(n-2)+1- \dim {\mathcal {M}}(L)$$ , where $${\mathcal {M}}(L)$$ denotes the Schur multiplier of L. For a non-abelian nilpotent Lie algebra, we know $$ s(L)\ge 0 $$ and the structure of all nilpotent Lie algebras are well known for $$ s(L) \in \lbrace 0,1,2,3 \rbrace $$ in several papers. The current paper is devoted to obtain the structure of all nilpotent Lie algebras L, when $$ s(L)=4 $$ .