Moonshine beyond the monster : the bridge connecting algebra, modular forms and physics

著者

    • Gannon, Terry

書誌事項

Moonshine beyond the monster : the bridge connecting algebra, modular forms and physics

Terry Gannon

（Cambridge monographs on mathematical physics）

Cambridge University Press, 2010

  • : pbk.

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注記

Includes bibliographical references (p. [445]-463) and index

Paperback's description based on digital printing 2010

内容説明・目次

内容説明

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.

目次

  • Acknowledgements
  • Introduction: glimpses of the theory beneath Monstrous moonshine
  • 1. Classical algebra
  • 2. Modular stuff
  • 3. Gold and brass: affine algebras and generalisations
  • 4. Conformal field theory: The physics of Moonshine
  • 5. Vertex operator algebras
  • 6. Modular group representations throughout the realm
  • 7. Monstrous Moonshine
  • Epilogue
  • Notation
  • References
  • Index.

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