Wockel, Christoph

[["dc.bibliographiccitation.firstpage","1273"],["dc.bibliographiccitation.issue","6"],["dc.bibliographiccitation.journal","Journal of the European Mathematical Society"],["dc.bibliographiccitation.lastpage","1320"],["dc.bibliographiccitation.volume","18"],["dc.contributor.author","Wockel, Christoph"],["dc.contributor.author","Zhu, Chenchang"],["dc.date.accessioned","2020-12-10T18:47:45Z"],["dc.date.available","2020-12-10T18:47:45Z"],["dc.date.issued","2016"],["dc.description.abstract","The purpose of this paper is to show how central extensions of (possibly infinite-dimensional) Lie algebras integrate to central extensions of étale Lie 2-groups in the sense of [Get09, Hen08]. In finite dimensions, central extensions of Lie algebras integrate to central extensions of Lie groups, a fact which is due to the vanishing of π 2 for each finite-dimensional Lie group. This fact was used by Cartan (in a slightly other guise) to construct the simply connected Lie group associated to each finite-dimensional Lie algebra. In infinite dimensions, there is an obstruction for a central extension of Lie algebras to integrate to a central extension of Lie groups. This obstruction comes from non-trivial π2 2 for general Lie groups. We show that this obstruction may be overcome by integrating central extensions of Lie algebras not to Lie groups but to central extensions of étale Lie 2-groups. As an application, we obtain a generalization of Lie’s Third Theorem to infinite-dimensional Lie algebras."],["dc.identifier.doi","10.4171/JEMS/613"],["dc.identifier.gro","3146465"],["dc.identifier.issn","1435-9855"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/78876"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.status","final"],["dc.relation.issn","1435-9855"],["dc.title","Integrating central extensions of Lie algebras via Lie 2-groups"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]