Belgian Math. Soc. Simon Stevin - 3, 21, 403-413 - August, 2014 - .

Publication year: 2014

We have recently shown that a nilpotent Lie algebra L of dimension n≥1 satisfies the inequality dim H2(L,Z)≤12(n+m−2)(n−m−1)+1, wheredim L2=m≥1 and H2(L,Z) is the 2-nd integral homology Lie algebra of L. Our first main result correlates this bound with the i-th Betti number dim Hi(L,C×) of L, where Hi(L,C×) denotes the i-th complex cohomology Lie algebra of L. Our second main result describes a more general restriction, which follows an idea of Ellis in [G. Ellis, The Schur multiplier of a pair of groups, Appl. Categ. Structures 6 (1998), 355–371].