Direct limits of regular Lie groups

Helge Glöckner

Mathematische Nachrichten, 2021, vol. 294, issue 1, 74-81

Abstract: Let G be a regular Lie group which is a directed union of regular Lie groups Gi (all modelled on possibly infinite‐dimensional, locally convex spaces). We show that G=lim⟶Gi as a regular Lie group if G admits a so‐called direct limit chart. Notably, this allows the regular Lie group Diffc(M) of compactly supported diffeomorphisms to be interpreted as a direct limit of the regular Lie groups DiffK(M) of diffeomorphisms supported in compact sets K⊆M, even if the finite‐dimensional smooth manifold M is merely paracompact (but not necessarily σ‐compact), which is new. Similar results are obtained for the test function groups Cck(M,F) with values in a Lie group F.

Date: 2021
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https://doi.org/10.1002/mana.201900073

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