Chiral Koszul duality

Details Chiral Koszul duality Chiral Koszul duality

2011-03-30

arxiv.org/abs/1103.5803v4

Mathematics

Algebraic Geometry

Scientific paper

We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld in \cite{bd}, 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 \cite{bd} on chiral enveloping algebras of $\star$-Lie algebras.

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