Geodesic
Integrating central extensions of Lie algebras via Lie 2-groups
Journal of the European Mathematical Society, Tome 18 (2016) no. 6, pp. 1273-1320 Cet article a éte moissonné depuis la source EMS Press

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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 π2​ 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.
DOI : 10.4171/jems/613
Classification : 22-XX, 55-XX, 58-XX
Keywords: Infinite-dimensional Lie group, central extension, smooth group cohomology, group stack, Lie 2-group, integration of cocycles, Lie’s Third Theorem, 2-connected cover 
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     author = {Christoph Wockel and Chenchang Zhu},
     title = {Integrating central extensions of {Lie} algebras via {Lie} 2-groups},
     journal = {Journal of the European Mathematical Society},
     pages = {1273--1320},
     year = {2016},
     volume = {18},
     number = {6},
     doi = {10.4171/jems/613},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/613/}
}
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Christoph Wockel; Chenchang Zhu. Integrating central extensions of Lie algebras via Lie 2-groups. Journal of the European Mathematical Society, Tome 18 (2016) no. 6, pp. 1273-1320. doi: 10.4171/jems/613

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