Some Generalized Kac-Moody Algebras With Known Root Multiplicities

Details Some Generalized Kac-Moody Algebras With Known Root Multiplicities Some Generalized Kac-Moody Algebras With Known Root Multiplicities

2000-01-05

arxiv.org/abs/math/0001029v1

Memoirs of the AMS, volume 157, number 746, 2002, 1-119

Mathematics

Quantum Algebra

123 pages, AMSLaTex v 1.2, documentclass memoirs

Scientific paper

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.

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