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Journal of Lie Theory 17 (2007), No. 4, 899--902
Copyright Heldermann Verlag 2007

Simplified Proofs for the Pro-Lie Group Theorem and the One-Parameter Subgroup Lifting Lemma

Helge Glöckner
Universität Paderborn, Institut für Mathematik, Warburger Str. 100, 33098 Paderborn, Germany

This note is devoted to the theory of projective limits of finite-dimensional Lie groups, as developed in the recent monograph of K. H. Hofmann and S. A. Morris ["The Lie Theory of Connected Pro-Lie Groups", EMS Publ. House 2007]. 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.

Keywords: Pro-Lie group, approximation by Lie groups, projective limit, one-parameter subgroup lifting.

MSC: 22A05, 22E20, 22E65

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