For a nilpotent Lie algebra L of dimension n and dim(L2)=m, we find
the upper bound dim(M(L))≤1/2(n+m−2)(n−m−1)+1, where M(L) denotes the
Schur multiplier of L. In case m=1 the equality holds if and only if
L≅H(1)⊕A, where A is an abelian Lie algebra of dimension n−3
and H(1) is the Heisenberg algebra of dimension 3.Comment: Paper in press in Comm. Algebra with small revision