Geodesic
Simplified Proofs for the Pro-Lie Group Theorem and the One-Parameter Subgroup Lifting Lemma
Journal of Lie theory, Tome 17 (2007) no. 4, pp. 899-902

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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.
Classification : 22A05, 22E20, 22E65
Mots-clés : Pro-Lie group, approximation by Lie groups, projective limit, one-parameter subgroup lifting 
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     author = {H. Gl�ckner },
     title = {Simplified {Proofs} for the {Pro-Lie} {Group} {Theorem} and the {One-Parameter} {Subgroup} {Lifting} {Lemma}},
     journal = {Journal of Lie theory},
     pages = {899--902},
     publisher = {mathdoc},
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     number = {4},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JLT_2007_17_4_JLT_2007_17_4_a8/}
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H. Gl�ckner . Simplified Proofs for the Pro-Lie Group Theorem and the One-Parameter Subgroup Lifting Lemma. Journal of Lie theory, Tome 17 (2007) no. 4, pp. 899-902. http://geodesic.mathdoc.fr/item/JLT_2007_17_4_JLT_2007_17_4_a8/