
eBook ISBN: | 978-1-4704-0339-3 |
Product Code: | MEMO/157/746.E |
List Price: | $62.00 |
MAA Member Price: | $55.80 |
AMS Member Price: | $37.20 |

eBook ISBN: | 978-1-4704-0339-3 |
Product Code: | MEMO/157/746.E |
List Price: | $62.00 |
MAA Member Price: | $55.80 |
AMS Member Price: | $37.20 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 157; 2002; 119 ppMSC: Primary 17
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 \(AE_3\).
ReadershipGraduate students and research mathematicians interested in nonassociative rings and algebras.
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Table of Contents
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Chapters
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Introduction
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1. Generalized Kac-Moody algebras
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2. Modular forms
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3. Lattices and their theta-functions
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4. The proof of Theorem 1.7
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5. The real simple roots
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6. Hyperbolic Lie algebras
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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.
-
Chapters
-
Introduction
-
1. Generalized Kac-Moody algebras
-
2. Modular forms
-
3. Lattices and their theta-functions
-
4. The proof of Theorem 1.7
-
5. The real simple roots
-
6. Hyperbolic Lie algebras