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 $AE_3$.
| ISBN: | 9780821828885 |
| Publication date: | 30th March 2002 |
| Author: | Peter Niemann |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 119 pages |
| Series: | Memoirs of the American Mathematical Society |
| Genres: |
Algebra |