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dc.contributor.authorFrancis, John
dc.contributor.authorGaitsgory, Dennis
dc.date.accessioned2012-12-12T19:15:37Z
dc.date.issued2012
dc.identifier.citationFrancis, John, and Dennis Gaitsgory. 2012. Chiral Koszul duality. Selecta Mathematica, n.s., 18(1): 27-87.en_US
dc.identifier.issn1420-9020en_US
dc.identifier.issn1022-1824en_US
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:10043337
dc.description.abstractWe 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.en_US
dc.description.sponsorshipMathematicsen_US
dc.language.isoen_USen_US
dc.publisherSpringeren_US
dc.relation.isversionofdoi:10.1007/s00029-011-0065-zen_US
dc.relation.hasversionhttp://arxiv.org/abs/1103.5803en_US
dash.licenseOAP
dc.subjectalgebraic geometryen_US
dc.subjectalgebraic topologyen_US
dc.subjectquantum algebraen_US
dc.subjectchiral algebrasen_US
dc.subjectchiral homologyen_US
dc.subjectfactorization algebrasen_US
dc.subjectconformal field theoryen_US
dc.subjectKoszul dualityen_US
dc.subjectoperadsen_US
dc.subject\(\infty \) categoriesen_US
dc.titleChiral Koszul Dualityen_US
dc.typeJournal Articleen_US
dc.description.versionAuthor's Originalen_US
dc.relation.journalSelecta Mathematicaen_US
dash.depositing.authorGaitsgory, Dennis
dc.date.available2012-12-12T19:15:37Z
dc.identifier.doi10.1007/s00029-011-0065-z*
dash.contributor.affiliatedGaitsgory, Dennis


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