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Some Generalized Kac-Moody Algebras with Known Root Multiplicities
Peter Niemann, Logica UK Ltd, London, UK

Memoirs of the American Mathematical Society
2002; 119 pp; softcover
Volume: 157
ISBN-10: 0-8218-2888-6
ISBN-13: 978-0-8218-2888-5
List Price: US$62
Individual Members: US$37.20
Institutional Members: US$49.60
Order Code: MEMO/157/746
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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 \(AE_3\).


Graduate students and research mathematicians interested in nonassociative rings and algebras.

Table of Contents

  • Introduction
  • Generalized Kac-Moody algebras
  • Modular forms
  • Lattices and their Theta-functions
  • The proof of Theorem 1.7
  • The real simple roots
  • Hyperbolic Lie algebras
  • Appendix A
  • Appendix B
  • Bibliography
  • Notation
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