Journal of Lie Theory

no. 4
Simplified Proofs for the Pro-Lie Group Theorem and the One-Parameter Subgroup Lifting Lemma
Journal of Lie Theory, Volume 17 (2007) no. 4, pp. 899-902
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.
DOI: 10.5802/jolt.477
Classification: 22A05, 22E20, 22E65
Keywords: Pro-Lie group, approximation by Lie groups, projective limit, one-parameter subgroup lifting 
@article{JOLT_2007_17_4_a8,
     author = {H. Gl\"ockner},
     title = {Simplified {Proofs} for the {Pro-Lie} {Group} {Theorem} and the {One-Parameter} {Subgroup} {Lifting} {Lemma}},
     journal = {Journal of Lie Theory},
     pages = {899--902},
     year = {2007},
     volume = {17},
     number = {4},
     doi = {10.5802/jolt.477},
     zbl = {1154.22004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.477/}
}
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H. Glöckner. Simplified Proofs for the Pro-Lie Group Theorem and the One-Parameter Subgroup Lifting Lemma. Journal of Lie Theory, Volume 17 (2007) no. 4, pp. 899-902. doi: 10.5802/jolt.477

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