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Direct limits of regular Lie groups

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  • Helge Glöckner

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.

Suggested Citation

  • Helge Glöckner, 2021. "Direct limits of regular Lie groups," Mathematische Nachrichten, Wiley Blackwell, vol. 294(1), pages 74-81, January.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:1:p:74-81
    DOI: 10.1002/mana.201900073
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