Some Generalized Kac-Moody Algebras with Known Root Multiplicities

Released on by Peter Niemann
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  • Some Generalized Kac-Moody Algebras with Known Root Multiplicities Book Detail

  • Author : Peter Niemann
  • Release Date : 2002
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 137
  • ISBN 13 : 0821828886
  • File Size : 40,40 MB
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Some Generalized Kac-Moody Algebras with Known Root Multiplicities by Peter Niemann PDF Summary

Book Description: Starting from Borcherds' fake monster Lie algebra, this text 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 $AE_3$.

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