## Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and PhysicsThis 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 | |

22 | |

Fig 19 Some trivial knots | 41 |

II n f+v | 76 |

Fig 128 The commutativity constraint c43 in Braid | 91 |

Fig 129 The YangBaxter equation | 92 |

Fig 131 Evaluation coevaluation and twist | 93 |

tollolton II+ | 102 |

X wew er 2 u | 196 |

4 | 226 |

1 0 2 0 2 | 238 |

a | 244 |

?? | 249 |

p | 260 |

defined by | 309 |

5 | 311 |

2 | 104 |

a | 109 |

R | 110 |

1 + 2XDg TI1+q 1q 226a | 131 |

3 | 176 |

Fig 32 The nontwisted affine CoxeterDynkin diagrams | 191 |

6 | 354 |

ja exp | 362 |

Fig 65 A typical identity | 366 |

7 | 402 |

T t 1 | 410 |

### Other editions - View all

Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms ... Terry Gannon No preview available - 2006 |

Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms ... Terry Gannon No preview available - 2010 |

### Common terms and phrases

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

### References to this book

Lie Algebras, Vertex Operator Algebras and Their Applications: International ... Yi-Zhi Huang,Kailash C. Misra No preview available - 2007 |