On dimension of the Schur multiplier of nilpotent Lie algebras

Abstract Let L be an n-dimensional non-abelian nilpotent Lie algebra and $$ s(L) = \frac{1} {2}(n - 1)(n - 2) + 1 - \dim M(L) $$ where M(L) is the Schur multiplier of L. In [Niroomand P., Russo F., A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra (in press)] it has been shown that s(L) ≥ 0 and the structure of all nilpotent Lie algebras has been determined when s(L) = 0. In the present paper, we will characterize all finite dimensional nilpotent Lie algebras with s(L) = 1; 2.