2004/03/04 by Helge Glockner, Glockner, Helge
Mathematics · #22E65 (Primary) 46T05 #57N40 #58B10 #58B25 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:22E65 #msc:46T05 #msc:57N40 #msc:58B10 #msc:58B25
paper · pdf · doi:10.48550/arxiv.math/0403093
33 pages (v2: Lemma 7.12 and Proposition 7.13 corrected, clearer distinction between analyticity and convenient analyticity)
arxiv created 2004/05/14 · arxiv updated 2009/12/01
We show that every countable direct system of finite-dimensional real or complex Lie groups has a direct limit in the category of Lie groups modelled on locally convex spaces. This enables us to push all basic constructions of finite-dimensional Lie theory to the case of direct limit groups. In particular, we obtain an analogue of Lie's third theorem: Every countable-dimensional real or complex locally finite Lie algebra is enlargible, i.e., it is the Lie algebra of some regular Lie group (a suitable direct limit group).