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Vertex Operator Algebras and the Monster - 1st Edition - ISBN: 9780122670657, 9780080874548

Vertex Operator Algebras and the Monster, Volume 134

1st Edition

Authors: Igor Frenkel James Lepowsky Arne Meurman
Hardcover ISBN: 9780122670657
eBook ISBN: 9780080874548
Imprint: Academic Press
Published Date: 28th March 1989
Page Count: 508
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Table of Contents

Lie Algebras. Formal Calculus: Introduction. Realizations of sl(2) by Twisted Vertex Operators. Realizations of sl(2) by Untwisted Vertex Operators. Central Extensions. The Simple Lie Algebras An, Dn, En. Vertex Operator Realizations of An, Dn, En. General Theory of Untwisted Vertex Operators. General Theory of Twisted Vertex Operators. The Moonshine Module. Triality. The Main Theorem. Completion of the Proof. Appendix: Complex Realization of Vertex Operator Algebras. Bibliography. Index of frequently used symbols. Index.


This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."


Research mathematicians, mathematical physicists, and graduate students.


No. of pages:
© Academic Press 1989
28th March 1989
Academic Press
Hardcover ISBN:
eBook ISBN:


@qu:This book is a detailed research monograph which contains the complete proofs of the authors' previously announced results. It is mostly self-contained and the exposition, given the technicalities involved, could not have been any better. It will be an asset to research mathematicians as well as physicists, and certainly deserves a place in every mathematics and physics library.
@qu:The present book shows how this group arises as the symmetry group of a certain vertex-operator algebra....'One fact, however, is undeniable. As the automorphism group of a distinguished conformal field theory, the Monster is fundamentally related to one of the most spectacular chapters of modern theoretical physics--string theroy.'
@source:--N.J.A. SLoane, AT&T Laboratories quoted in AMERICAN SCIENTIST

Ratings and Reviews

About the Authors

Igor Frenkel

Affiliations and Expertise

Yale University, New Haven, Connecticut

James Lepowsky

Affiliations and Expertise

Rutgers University

Arne Meurman

Affiliations and Expertise

University of Stockholm