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Introduction

  • Yi-Zhi Huang
Chapter
Part of the Progress in Mathematics book series (PM, volume 148)

Abstract

The notion of vertex algebra, introduced by Borcherds [Bo] in a mathematical setting, and by Prenkel, Lepowsky and Meurman [FLM2] in the modified form, “vertex operator algebra,” that we will need to use in the present work, arose naturally in Frenkel, Lepowsky and Meurman’s vertex operator construction [FLM1] [FLM2] of the Monster sporadic finite simple group [Gr]. In fact, they realized the Monster as the symmetry group of a special vertex operator algebra, the “moonshine module.” (See the introduction of [FLM2] for a historical discussion, including the important contribution of Borcherds’ announcement [Bo].) Meanwhile, conformai field theory, a physical theory whose algebraic structure was developed systematically by Belavin, Polyakov and Zamolodchikov [BPZ] in a physical context, has been becoming more and more attractive to mathematicians. In the study of conformal field theories, physicists also arrived at, though perhaps without a completely rigorous definition, the notion of “chiral algebra,” a notion which essentially coincides with the notion of vertex operator algebra (see e.g. [MS]).

Keywords

Modulus Space Riemann Surface Vertex Operator Conformal Field Theory Vertex Operator Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser 1997

Authors and Affiliations

  • Yi-Zhi Huang
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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