Vertex Operator Algebras and the Monster

Vertex Operator Algebras and the Monster

1st Edition - March 28, 1989
This is the Latest Edition
  • Authors: Igor Frenkel, James Lepowsky, Arne Meurman
  • Hardcover ISBN: 9780122670657
  • eBook ISBN: 9780080874548

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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.

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.

Product details

  • No. of pages: 508
  • Language: English
  • Copyright: © Academic Press 1989
  • Published: March 28, 1989
  • Imprint: Academic Press
  • Hardcover ISBN: 9780122670657
  • eBook ISBN: 9780080874548
  • 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