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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)

Abstract

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.

Keywords

Open Subset Variable Approach Inverse Image Operator Product Expansion Jacobi Identity 
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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References

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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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