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


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]).


Modulus Space Riemann Surface Vertex Operator Conformal Field Theory Vertex Operator Algebra 
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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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