Chiral Koszul duality

John Francis*, Dennis Gaitsgory

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

Abstract

We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004), to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and factorization structures, in a sense analogous to Quillen's homotopy theory of differential graded Lie algebras. We prove the equivalence of higher-dimensional chiral and factorization algebras by embedding factorization algebras into a larger category of chiral commutative coalgebras, then realizing this interrelation as a chiral form of Koszul duality. We apply these techniques to rederive some fundamental results of Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004) on chiral enveloping algebras of {black star}-Lie algebras.

Original languageEnglish (US)
Pages (from-to)27-87
Number of pages61
JournalSelecta Mathematica, New Series
Volume18
Issue number1
DOIs
StatePublished - Mar 2012

Keywords

  • Chiral algebras
  • Chiral homology
  • Conformal field theory
  • Factorization algebras
  • Koszul duality
  • Operads
  • ∞-Categories

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy

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