2020
DOI: 10.1002/mana.201900073
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Direct limits of regular Lie groups

Abstract: Let G be a regular Lie group which is a directed union of regular Lie groups (all modelled on possibly infinite‐dimensional, locally convex spaces). We show that as a regular Lie group if G admits a so‐called direct limit chart. Notably, this allows the regular Lie group of compactly supported diffeomorphisms to be interpreted as a direct limit of the regular Lie groups of diffeomorphisms supported in compact sets , even if the finite‐dimensional smooth manifold M is merely paracompact (but not necessarily… Show more

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Cited by 1 publication
(2 citation statements)
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“…Example 1.3 For m ∈ N, k ∈ N 0 , and α ∈ ]0, 1], Proposition 1.1 can be applied to the Banach spaces F (U, R) := C k,α (U, R) of k times Hölderdifferentiable functions on bounded open subsets U ⊆ R m (see [18]). This yields Banach-Lie groups C k,α (M, G) := F (M, G) with properties as described in the proposition.…”
Section: Introduction and Statement Of Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…Example 1.3 For m ∈ N, k ∈ N 0 , and α ∈ ]0, 1], Proposition 1.1 can be applied to the Banach spaces F (U, R) := C k,α (U, R) of k times Hölderdifferentiable functions on bounded open subsets U ⊆ R m (see [18]). This yields Banach-Lie groups C k,α (M, G) := F (M, G) with properties as described in the proposition.…”
Section: Introduction and Statement Of Resultsmentioning
confidence: 99%
“…See [36] for a characterization. Example 1.4 For m = 1 and p ∈ [1, ∞], Proposition 1.1 can be applied to the Banach spaces F (U, R) := AC L p (U, R) of absolutely continuous functions with L p -derivatives on bounded open intervals U = ∅ in R (see [18]). For M := S the unit circle, this yields Banach-Lie groups AC L p (S, G) := F (S, G) with properties as described in the proposition.…”
Section: Introduction and Statement Of Resultsmentioning
confidence: 99%