Proper affine actions on semisimple Lie algebras  [ Actions affines propres sur les algèbres de Lie semisimples ]
Annales de l'Institut Fourier, Tome 66 (2016) no. 2, pp. 785-831.

Pour tout groupe de Lie réel semisimple non compact G, on construit un groupe discret de transformations affines de son algèbre de Lie 𝔤 dont la partie linéaire est Zariski-dense dans AdG et qui est libre, non abélien et agit proprement sur 𝔤.

For any noncompact semisimple real Lie group G, we construct a group of affine transformations of its Lie algebra 𝔤 whose linear part is Zariski-dense in AdG and which is free, nonabelian and acts properly discontinuously on 𝔤.

Reçu le : 2014-06-18
Révisé le : 2015-06-18
Accepté le : 2015-09-09
Publié le : 2016-02-16
DOI : https://doi.org/10.5802/aif.3026
Classification : 20G20,  22E40,  20H15
Mots clés : Sous-groupes discrets de groups de Lie, groupes affines, conjecture d’Auslander, conjecture de Milnor, variétés affines plates, représentation adjointe, invariant de Margulis, quasi-translation, groupe libre, groupe de Schottky
@article{AIF_2016__66_2_785_0,
     author = {Smilga, Ilia},
     title = {Proper affine actions on semisimple Lie algebras},
     journal = {Annales de l'Institut Fourier},
     pages = {785--831},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {2},
     year = {2016},
     doi = {10.5802/aif.3026},
     language = {en},
     url = {www.numdam.org/item/AIF_2016__66_2_785_0/}
}
Smilga, Ilia. Proper affine actions on semisimple Lie algebras. Annales de l'Institut Fourier, Tome 66 (2016) no. 2, pp. 785-831. doi : 10.5802/aif.3026. http://www.numdam.org/item/AIF_2016__66_2_785_0/

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