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Moonshine, the Monster, and Related Topics
Edited by: Chongying Dong, and Geoffrey Mason, University of California, Santa Cruz, CA
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Contemporary Mathematics
1996; 368 pp; softcover
Volume: 193
ISBN-10: 0-8218-0385-9
ISBN-13: 978-0-8218-0385-1
List Price: US$86
Member Price: US$68.80
Order Code: CONM/193
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"One of the great legacies of the classification of the finite simple groups is the existence of the Monster \(\ldots\) Work of Borcherds and Frenkel-Lepowsky-Meurman led to the notion of a vertex (operator) algebra, which was seen to be the same as the chiral algebras used by physicists in conformal field theory\(\ldots\) The connections with physics have proven to be invaluable, and it seems likely that another branch of mathematics whose origins are eerily similar to those of moonshine--that is, elliptic cohomology--will turn out to be very relevant too. -- from the Preface

This volume contains the proceedings of a Joint Summer Research Conference held at Mount Holyoke College in June 1994. As perhaps the first conference proceedings devoted exclusively to the subject known as "Moonshine", this work contains something for many mathematicians and physicists.

Features:

  • Results concerning the monster simple group and other simple groups.
  • Connections with elliptic cohomology.
  • Connections with 2-dimensional conformal field theory.
  • The role of operads.
  • Connections with modular functions.

Much of Moonshine, the Monster, and Related Topics features new results not available anywhere else.

Readership

Research mathematicians and theoretical physicists interested in the connections among finite groups.

Table of Contents

  • P. Bántay -- Higher genus moonshine
  • L. Dolan -- Superstring twisted conformal field theory
  • C. Dong, H. Li, and G. Mason -- Some twisted sectors for the moonshine module
  • A. J. Feingold, J. X. Ries, and M. D. Weiner -- Spinor construction of the \(c=1/2\) minimal model
  • K. Harada and M. L. Lang -- The McKay-Thompson series associated with the irreducible characters of the monster
  • T. Hsu -- Some quilts for the Mathieu groups
  • Y.-Z. Huang -- A nonmeromorphic extension of the moonshine module vertex operator algebra
  • A. A. Ivanov -- On the Buekenhout-Fischer geometry of the monster
  • T. Kimura -- Operads of moduli spaces and algebraic structures in conformal field theory
  • J. Lepowsky and R. L. Wilson -- On Hopf algebras and the elimination theorem for free Lie algebras
  • H.-S. Li -- Local systems of twisted vertex operators, vertex operator superalgebras and twisted modules
  • K. Liu -- Modular forms and topology
  • Y. Martin -- On modular invariance of completely replicable functions
  • K. C. Misra -- On embedding of integrable highest weight modules of affine Lie algebras
  • S. Norton -- The monster algebra: Some new formulae
  • A. E. Ryba -- Modular moonshine?
  • G. W. Smith -- Replicant powers for higher genera
  • M. P. Tuite -- Generalised moonshine and Abelian orbifold constructions
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