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Publisher:
Cambridge University Press
Online publication date:
July 2023
Print publication year:
2023
Online ISBN:
9781009401548
Creative Commons:
Creative Common License - CC Creative Common License - BY Creative Common License - NC Creative Common License - ND
This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC-ND 4.0 https://creativecommons.org/creativelicenses

Book description

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 more than 100 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. Originally published in 2006, this title has been reissued as an Open Access publication on Cambridge Core.

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Contents

Full book PDF
  • Frontmatter
    pp i-iv
  • Dedication
    pp v-vi
  • Contents
    pp vii-xii
  • Acknowledgments
    pp xiii-xiv
  • 0 - Introduction: glimpses of the theory beneath Monstrous Moonshine
    pp 1-13
  • 1 - Classical algebra
    pp 14-103
  • 2 - Modular stuff
    pp 104-175
  • 3 - Gold and brass: affine algebras and generalisations
    pp 176-225
  • 4 - Conformal field theory: the physics of Moonshine
    pp 226-310
  • 5 - Vertex operator algebras
    pp 311-353
  • 6 - Modular group representations throughout the realm
    pp 354-401
  • 7 - Monstrous Moonshine
    pp 402-434
  • Epilogue, or the squirrel who got away?
    pp 435-435
  • Notation
    pp 436-444
  • References
    pp 445-463
  • Index
    pp 464-478

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