Chiral Koszul duality

By J. Francis, D. Gaitsgory. 2011

122 citations recorded by the source corpus.

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 $${\star}$$ -Lie algebras.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ae3708b006d1f7fb77d9353cc946aca714a5a28d

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In Geometry and Topology

1. D. Gaitsgory
2. V. Drinfeld
3. J. Francis
4. V. Hinich
5. Gijs Heuts
6. Ieke Moerdijk
7. Daniel Halpern-Leistner
8. D. Nadler

In Mathematical Physics

1. D. Gaitsgory
2. V. Drinfeld
3. V. Hinich
4. J. Francis
5. Gijs Heuts
6. Ieke Moerdijk
7. Daniel Halpern-Leistner
8. D. Nadler

In Statistical and Nonlinear Physics

1. V. Drinfeld
2. J. Francis
3. D. Gaitsgory

Citations in the corpus

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