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The geometric understanding of Cartan connections led Charles Ehresmann from the Erlangen program of (abstract) transformation groups to the enlarged program of Lie groupoid actions, via the basic concept of structural groupoid acting through the fibres of a (smooth) principal fibre bundle or of its associated bundles, and the basic examples stemming from the manifold of jets (fibred by its source or target projections). We show that the remarkable relation arising between the actions of the structural...
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 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...
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