Linking Lie groupoid representations and representations of infinite-dimensional Lie groups (Q2417926)

In this paper, the authors show that smooth representations of Lie groupoids produce representations of associated Lie groups. These groups are the bisection group and a group of groupoid self-maps. \par So, representations of the Lie groupoids produce representations of the infinite-dimensional Lie groups on spaces of (compactly supported) bundle sections. Endowing the spaces of bundle sections with a fine Whitney type topology, the authors obtain indeed continuous and smooth representations. \par In the topological category, this correspondence can be reversed for certain topological groupoids. The authors extend this result to the smooth category under weaker assumptions on the groupoids.