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 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."
--MATHEMATICAL REVIEWS
"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." --N.J.A. SLoane, AT&T Laboratories quoted in AMERICAN
SCIENTIST
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