# Linking Lie groupoid representations and representations of infinite-dimensional Lie groups

@article{Amiri2019LinkingLG, title={Linking Lie groupoid representations and representations of infinite-dimensional Lie groups}, author={Habib Amiri and Alexander Schmeding}, journal={Annals of Global Analysis and Geometry}, year={2019}, volume={55}, pages={749-775} }

The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged here are the bisection group and a group of groupoid self-maps. Then, representations of the Lie groupoids give rise to representations of the infinite-dimensional Lie groups on spaces of (compactly supported) bundle sections. Endowing the spaces of bundle… Expand

#### 3 Citations

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Abstract In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and… Expand

Lie groupoids of mappings taking values in a Lie groupoid

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Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are… Expand

A differentiable monoid of smooth maps on Lie groupoids

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In this article we investigate a monoid of smooth mappings on the space of arrows of a Lie groupoid and its group of units. The group of units turns out to be an infinite-dimensional Lie group which… Expand

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