# Moonshine, the Monster, and Related Topics

Share this page *Edited by *
*Chongying Dong; Geoffrey Mason*

“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

#### Readership

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

# Table of Contents

## Moonshine, the Monster, and Related Topics

- Contents vii8 free
- Preface ix10 free
- Higher genus Moonshine 112 free
- Superstring twisted conformal field theory 920
- Some twisted sectors for the Moonshine Module 2536
- Spinor construction of the c = 1/2 minimal model 4556
- The McKay-Thompson series associated with the irreducible characters of the Monster 93104
- Some quilts for the Mathieu groups 113124
- A nonmeromorphic extension of the Moonshine Module vertex operator algebra 123134
- On the Buekenhout-Fischer geometry of the Monster 149160
- Operads of moduli spaces and algebraic structures in conformal field theory 159170
- On Hopf algebras and the elimination theorem for free Lie algebras 191202
- Local systems of twisted vertex operators, vertex operator superalgebras and twisted modules 203214
- Modular forms and topology 237248
- On modular invariance of completely replicable functions 263274
- On embedding of integrable highest weight modules of affine Lie algebras 287298
- The monster algebra: Some new formulae 297308
- Modular Moonshine? 307318
- Replicant powers for higher genera 337348
- Generalised Moonshine and abelian orbifold constructions 353364