Lie group structures on groups of diffeomorphisms and applications to CR manifolds
[Sous-groupes de difféomorphismes, leur structure de groupe de Lie, et applications aux variétés CR.]
Annales de l'Institut Fourier, Tome 54 (2004) no. 5, pp. 1279-1303.

Nous donnons des conditions suffisantes pour qu’un sous-groupe donné du groupe des difféomorphismes d’une variété indéfiniment differentiable ou réelle analytique ait une structure compatible de groupe de Lie. En utilisant ces résultats, ainsi que des travaux récents concernant la paramétrisation des automorphismes CR par leur jets en un point et leur systèmes complets, nous donnons des conditions sous lesquelles le groupe des automorphismes CR globaux d’une variété CR est un groupe de Lie relativement à une topologie appropriée.

We give general sufficient conditions to guarantee that a given subgroup of the group of diffeomorphisms of a smooth or real-analytic manifold has a compatible Lie group structure. These results, together with recent work concerning jet parametrization and complete systems for CR automorphisms, are then applied to determine when the global CR automorphism group of a CR manifold is a Lie group in an appropriate topology.

Classification : 22E15,  22F50,  32V20,  32V40,  57S25,  58D05
Mots clés : groupe de Lie, variété CR, automorphisme CR, jets, système complet.
     author = {Baouendi, M. Salah and Preiss Rothschild, Linda and Winkelmann, J\"org and Zaitsev, Dimitri},
     title = {Lie group structures on groups of diffeomorphisms and applications to {CR} manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {1279--1303},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {5},
     year = {2004},
     doi = {10.5802/aif.2050},
     zbl = {1062.22046},
     mrnumber = {2127849},
     language = {en},
     url = {}
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Baouendi, M. Salah; Preiss Rothschild, Linda; Winkelmann, Jörg; Zaitsev, Dimitri. Lie group structures on groups of diffeomorphisms and applications to CR manifolds. Annales de l'Institut Fourier, Tome 54 (2004) no. 5, pp. 1279-1303. doi : 10.5802/aif.2050.

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