Chiral Koszul duality [article]

John Francis, Dennis Gaitsgory
2011 arXiv   pre-print
We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld in 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
more » ... lgebras, then realizing this interrelation as a chiral form of Koszul duality. We apply these techniques to rederive some fundamental results of bd on chiral enveloping algebras of -Lie algebras.
arXiv:1103.5803v4 fatcat:xyaevwh54fb4bgiff7tgtkggce