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

Abstract

Let L be a non-abelian nilpotent Lie algebra of dimension n and $$s(L)=\\frac{1}{2}(n-1)(n-2)+1- \\dim {\\mathcal {M}}(L)$$s(L)=12(n-1)(n-2)+1-dimM(L), where $${\\mathcal {M}}(L)$$M(L) denotes the Schur multiplier of L. For a non-abelian nilpotent Lie algebra, we know $$ s(L)\\ge 0 $$s(L)≥0 and the structure of all nilpotent Lie algebras are well known for $$ s(L) \\in \\lbrace 0,1,2,3 \\rbrace $$s(L)∈{0,1,2,3} in several papers. The current paper is devoted to obtain the structure of all nilpotent Lie algebras L, when $$ s(L)=4 $$s(L)=4.