Some Generalized Kac-Moody Algebras with Known Root Multiplicities (Memoirs of the American Mathematical Society)

Some Generalized Kac-Moody Algebras with Known Root Multiplicities (Memoirs of the American Mathematical Society)

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Description

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 $AE_3$.

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.

Product Details

  • ISBN13: 9780821828885
  • Format: Paperback
  • ID: 9780821828885
  • ISBN10: 0821828886

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