Direct limits of infinite-dimensional Lie groups

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dc.creatorGlockner, Helge
dc.date2008-03-01
dc.date2008-04-01
dc.date.accessioned2026-07-07T09:29:17Z
dc.date.available2026-07-07T09:29:17Z
dc.descriptionMany infinite-dimensional Lie groups of interest can be expressed as a union of an ascending sequence of (finite- or infinite-dimensional) Lie groups. In this survey article, we compile general results concerning such ascending unions, describe the main classes of examples, and explain what the general theory tells us about these. In particular, we discuss: (1) Direct limit properties of ascending unions of Lie groups in the relevant categories; (2) Regularity in Milnor's sense; (3) Homotopy groups of direct limit groups and of Lie groups containing a dense union of Lie groups; (4) Subgroups of direct limit groups; (5) Constructions of Lie group structures on ascending unions of Lie groups.
dc.descriptionsurvey article, 38 pages, LaTeX (v2: minor revisions)
dc.identifierhttps://arxiv.org/abs/0803.0045
dc.identifierhttp://arxiv.org/abs/0803.0045
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157728
dc.subjectGroup Theory
dc.subjectFunctional Analysis
dc.subject22E65 (Primary); 26E15, 46A13, 46G20, 46T05, 46T20, 46T25, 54B35, 54D50, 55Q10, 58B05, 58D05 (Secondary)
dc.titleDirect limits of infinite-dimensional Lie groups
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