Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories

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dc.creatorGlockner, Helge
dc.date2006-06-03
dc.date.accessioned2026-07-07T07:14:46Z
dc.date.available2026-07-07T07:14:46Z
dc.descriptionLet G be a Lie group which is the union of an ascending sequence of Lie groups G_n (all of which may be infinite-dimensional). We study the question when G is the direct limit of the G_n's in the category of Lie groups, topological groups, smooth manifolds, resp., topological spaces. Full answers are obtained for G the group Diff_c(M) of compactly supported smooth diffeomorphisms of a sigma-compact smooth manifold M, and for test function groups C^infty_c(M,H) of compactly supported smooth maps with values in a finite-dimensional Lie group H. We also discuss the cases where G is a direct limit of unit groups of Banach algebras, a Lie group of germs of Lie group-valued analytic maps, or a weak direct product of Lie groups.
dc.descriptionextended preprint version, 66 pages
dc.identifierhttps://arxiv.org/abs/math/0606078
dc.identifierhttp://arxiv.org/abs/math/0606078
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113015
dc.subjectGroup Theory
dc.subjectFunctional Analysis
dc.subject22E65 (Primary) 22E67, 46A13, 46F05, 46T20, 54B30, 54H11, 58B10, 58D05
dc.titleDirect limits of infinite-dimensional Lie groups compared to direct limits in related categories
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