2019/02/17 by Glockner, Helge
#22E65 (primary) #22E66 #22E67 #46M40 #46T10 (secondary) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1902.06329
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 is the direct limit of the Gi as a regular Lie group whenever G admits a so-called direct limit chart. Notably, this allows the regular Lie group Diffc(M) of compactly supported smooth diffeomorphisms to be interpreted as a direct limit of the regular Lie groups DiffK(M) of smooth diffeomorphisms supported in compact subsets K of M, even if the finite-dimensional smooth manifold M is merely paracompact (but not necessarily sigma-compact), which was not known before. Similar results are obtained for the test function groups Ckc(M,F) with values in a Lie group F.