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The Lie group of real analytic diffeomorphisms is not real analytic

Rafael Dahmen;  Alexander Schmeding — 2015

Studia Mathematica

We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense of Milnor. ...

Lie groupoids of mappings taking values in a Lie groupoid

Habib Amiri;  Helge Glöckner;  Alexander Schmeding — 2020

Archivum Mathematicum

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 prime examples of infinite-dimensional Lie groups modelled on locally convex spaces. In the present paper, we generalise this construction and show that differentiable mappings on a compact manifold (possibly with boundary) with values in a Lie groupoid form infinite-dimensional Lie groupoids which we...

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