dorsal/arxiv
View SchemaOn the D-module and formal-variable approaches to vertex algebras
| Authors | Yi-Zhi Huang, James Lepowsky |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9603020 |
| URL | https://arxiv.org/abs/q-alg/9603020 |
| Journal | Topics in Geometry: In Memory of Joseph D'Atri, ed. S. Gindikin, Progress in Nonlinear Differential Equations, Vol. 20, Birkhauser, Boston, 1996. 175--202 |
Abstract
In 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.
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"abstract": "In a program to formulate and develop two-dimensional conformal field theory\nin the framework of algebraic geometry, Beilinson and Drinfeld have recently\ngiven a notion of ``chiral algebra\u0027\u0027 in terms of D-modules on algebraic curves.\nThis definition consists of a ``skew-symmetry\u0027\u0027 relation and a ``Jacobi\nidentity\u0027\u0027 relation in a categorical setting. In this paper, we show directly\nthat these chiral algebras are essentially the same as vertex algebras without\nvacuum vector (and without grading), by establishing an equivalence between the\nskew-symmetry and Jacobi identity relations of Beilinson-Drinfeld and the\n(similarly-named, but different) skew-symmetry and Jacobi identity relations in\nthe formal-variable approach to vertex operator algebra theory as formulated by\nBorcherds, Frenkel-Lepowsky-Meurman and Frenkel-Huang-Lepowsky.",
"arxiv_id": "q-alg/9603020",
"authors": [
"Yi-Zhi Huang",
"James Lepowsky"
],
"categories": [
"q-alg",
"alg-geom",
"hep-th",
"math.AG",
"math.QA"
],
"journal_ref": "Topics in Geometry: In Memory of Joseph D\u0027Atri, ed. S. Gindikin,\n Progress in Nonlinear Differential Equations, Vol. 20, Birkhauser, Boston,\n 1996. 175--202",
"title": "On the D-module and formal-variable approaches to vertex algebras",
"url": "https://arxiv.org/abs/q-alg/9603020"
},
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