
Journal of Lie Theory 17 (2007), No. 4, 899902 Copyright Heldermann Verlag 2007 Simplified Proofs for the ProLie Group Theorem and the OneParameter Subgroup Lifting Lemma Helge Glöckner Universität Paderborn, Institut für Mathematik, Warburger Str. 100, 33098 Paderborn, Germany glockner@math.unipaderborn.de This note is devoted to the theory of projective limits of finitedimensional Lie groups, as developed in the recent monograph of K. H. Hofmann and S. A. Morris ["The Lie Theory of Connected ProLie Groups", EMS Publ. House 2007]. We replace the original, highly nontrivial proof of the OneParameter Subgroup Lifting Lemma given in the monograph by a shorter and more elementary argument. Furthermore, we shorten (and correct) the proof of the socalled ProLie Group Theorem, which asserts that proLie groups and projective limits of Lie groups coincide. Keywords: ProLie group, approximation by Lie groups, projective limit, oneparameter subgroup lifting. MSC: 22A05, 22E20, 22E65 [ Fulltextpdf (130 KB)] for subscribers only. 