Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics

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Cambridge University Press, Sep 7, 2006 - Science
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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

1
14
1 1 0 1 0 1
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

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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.

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