2000/01/05 by Peter Niemann
Mathematics · #math.QA #msc:17B65
published as Memoirs of the AMS, volume 157, number 746, 2002, 1-119 · 123 pages, AMSLaTex v 1.2, documentclass memoirs
arxiv created 2000/01/05 · arxiv updated 2009/11/30
Starting from Borcherds' fake monster Lie algebra we construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including AE3.