Vertex Operator Algebras and the Monster

Igor Frenkel (Author), James Lepowsky (Author), Arne Meurman (Author)

9780122670657, Elsevier Science

Hardback, published 1 May 1989

508 pages
22.9 x 15.2 x 3 cm, 0.92 kg

"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

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."

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.

Subject Areas: Real analysis, real variables [PBKB], Algebra [PBF]