On the D-Module and Formal-Variable Approaches to Vertex Algebras

  • Yi-Zhi Huang
  • James Lepowsky
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 20)


In a program to formulate and develop two-dimensional conformal field theory in the framework of algebraic geometry, Beilinson and Drinfeld [BD] have recently given a notion of “chiral algebra” in terms of D-modules on algebraic curves. This definition consists of a “skew-symmetry” relation and a “Jacobi identity” relation in a categorical setting, and it leads to the operator product expansion for holomorphic quantum fields in the spirit of two-dimensional conformal field theory, as expressed in [BPZ], Because this operator product expansion, properly formulated, is known to be essentially a variant of the main axiom, the “Jacobi identity” [FLM], for vertex (operator) algebras ([Borc], [FLM]; see [FLM] for the proof), the chiral algebras of [BD] amount essentially to vertex algebras.


Open Subset Variable Approach Inverse Image Operator Product Expansion Jacobi Identity 
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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Yi-Zhi Huang
    • 1
  • James Lepowsky
    • 1
  1. 1.Department of MatematicsRutgers UniversityNew BrunswickUSA

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