On the D-module and formal-variable approaches to vertex algebras

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dc.creatorHuang, Yi-Zhi
dc.creatorLepowsky, James
dc.date1996-03-23
dc.date.accessioned2026-07-07T09:16:53Z
dc.date.available2026-07-07T09:16:53Z
dc.descriptionIn a program to formulate and develop two-dimensional conformal field theory in the framework of algebraic geometry, Beilinson and Drinfeld 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. In this paper, we show directly that these chiral algebras are essentially the same as vertex algebras without vacuum vector (and without grading), by establishing an equivalence between the skew-symmetry and Jacobi identity relations of Beilinson-Drinfeld and the (similarly-named, but different) skew-symmetry and Jacobi identity relations in the formal-variable approach to vertex operator algebra theory as formulated by Borcherds, Frenkel-Lepowsky-Meurman and Frenkel-Huang-Lepowsky.
dc.description31 pages, LaTeX file
dc.identifierhttps://arxiv.org/abs/q-alg/9603020
dc.identifierhttp://arxiv.org/abs/q-alg/9603020
dc.identifierTopics in Geometry: In Memory of Joseph D'Atri, ed. S. Gindikin, Progress in Nonlinear Differential Equations, Vol. 20, Birkhauser, Boston, 1996. 175--202
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153513
dc.subjectQuantum Algebra
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.titleOn the D-module and formal-variable approaches to vertex algebras
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