P. Niroomand , F.G. Russo
Belgian Math. Soc. Simon Stevin - 3, 21, 403-413 - August, 2014 - .
Publication year: 2014

#### Abstract

We have recently shown that a nilpotent Lie algebra of dimension satisfies the inequality , where and is the 2-nd integral homology Lie algebra of . Our first main result correlates this bound with the -th Betti number of , where denotes the -th complex cohomology Lie algebra of . 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].