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Postcards from the Edge, or Snapshots of the Theory of Generalised Moonshine

  Published:2002-12-01
 Printed: Dec 2002
  • Terry Gannon
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Abstract

We begin by reviewing Monstrous Moonshine. The impact of Moonshine on algebra has been profound, but so far it has had little to teach number theory. We introduce (using `postcards') a much larger context in which Monstrous Moonshine naturally sits. This context suggests Moonshine should indeed have consequences for number theory. We provide some humble examples of this: new generalisations of Gauss sums and quadratic reciprocity.
MSC Classifications: 11F22, 17B67, 81T40 show english descriptions Relationship to Lie algebras and finite simple groups
Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
Two-dimensional field theories, conformal field theories, etc.
11F22 - Relationship to Lie algebras and finite simple groups
17B67 - Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
81T40 - Two-dimensional field theories, conformal field theories, etc.
 

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