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Some Generalized Kac-Moody Algebras with Known Root Multiplicities
 
Peter Niemann Logica UK Ltd, London, UK
Some Generalized Kac-Moody Algebras with Known Root Multiplicities
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
Some Generalized Kac-Moody Algebras with Known Root Multiplicities
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Some Generalized Kac-Moody Algebras with Known Root Multiplicities
Peter Niemann Logica UK Ltd, London, UK
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1572002; 119 pp
    MSC: 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 \(AE_3\).

    Readership

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

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1572002; 119 pp
MSC: 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 \(AE_3\).

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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