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- W4288574888 abstract "Let G be a regular Lie group which is a directed union of regular Lie groups G_i (all modelled on possibly infinite-dimensional, locally convex spaces). We show that G is the direct limit of the G_i as a regular Lie group whenever G admits a so-called direct limit chart. Notably, this allows the regular Lie group Diff_c(M) of compactly supported smooth diffeomorphisms to be interpreted as a direct limit of the regular Lie groups Diff_K(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 C^k_c(M,F) with values in a Lie group F." @default.
- W4288574888 created "2022-07-29" @default.
- W4288574888 creator A5040391008 @default.
- W4288574888 date "2019-02-17" @default.
- W4288574888 modified "2023-10-16" @default.
- W4288574888 title "Direct limits of regular Lie groups" @default.
- W4288574888 doi "https://doi.org/10.48550/arxiv.1902.06329" @default.
- W4288574888 hasPublicationYear "2019" @default.
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