## Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics (Google eBook)This book was originally published in 2006. Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory. |

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### Contents

14 | |

35 | |

Fig 128 The commutativity constraint c43 in Braid | 91 |

2 | 104 |

a | 109 |

R | 110 |

3 | 176 |

4 | 226 |

?? | 249 |

x | 251 |

5 | 311 |

6 | 354 |

### Common terms and phrases

abelian afﬁne algebra algebra g analogue automorphism braid group called central extension character chiral blocks classical coefﬁcients commutative complex conformal ﬁeld theory Conjecture construction corresponding Coxeter–Dynkin diagram deﬁned Deﬁnition diagram eigenvalues equation equivalent example ﬁnd ﬁnite group ﬁnite-dimensional ﬁrst ﬁxed formula fusion ring Galois generalisation genus geometry given graded dimension group G Hauptmodul highest-weight Hilbert space holomorphic identiﬁed identity inﬁnite integral isomorphic Kac–Moody algebras lattice Lie group linear manifold mathematics matrix modular data modular forms modular functions modular invariants moduli space Monstrous Moonshine Moonshine module multiplicities obeying one-dimensional orbifold parametrised particle physics polynomial projective representation quantum ﬁeld theory Question quotient RCFT reﬂection roots Section semi-simple simple Lie algebras space-time string theory structure subalgebra subgroup symmetry Theorem topological torus trivial twisted unique unitary V-module vector space Verma module weight Weyl group

### Popular passages

Page 34 - The angle between two intersecting curves is defined to be the angle between the tangents to the curves at their point of intersection.