Some Generalized Kac-Moody Algebras With Known Root Multiplicities
Quantum Algebra
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0001029,
title = {Some Generalized Kac-Moody Algebras With Known Root Multiplicities},
author = {Peter Niemann},
journal= {arXiv preprint arXiv:math/0001029},
year = {2007}
}
Comments
123 pages, AMSLaTex v 1.2, documentclass memoirs