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.
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© 1996 Birkhäuser Boston
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Huang, YZ., Lepowsky, J. (1996). On the D-Module and Formal-Variable Approaches to Vertex Algebras. In: Gindikin, S. (eds) Topics in Geometry. Progress in Nonlinear Differential Equations and Their Applications, vol 20. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2432-7_5
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