2007/09/14 by Helge Glöckner, Helge Glockner, Glockner, Helge
Mathematics · #22A05 (Primary) #22E15 #22E65 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:22A05 #msc:22E15 #msc:22E65
paper · pdf · doi:10.48550/arxiv.0709.2371
4 pages, LaTeX (v3: slightly expanded)
openalex publication_date 2007/09/14 · arxiv created 2007/09/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note is devoted to the theory of projective limits of finite-dimensional Lie groups, as developed in the recent monograph ``The Lie Theory of Connected Pro-Lie Groups'' by K.H. Hofmann and S.A. Morris. We replace the original, highly non-trivial proof of the One-Parameter Subgroup Lifting Lemma given in the monograph by a shorter and more elementary argument. Furthermore, we shorten (and correct) the proof of the so-called Pro-Lie Group Theorem, which asserts that pro-Lie groups and projective limits of Lie groups coincide.