Pour tout groupe de Lie réel semisimple non compact , on construit un groupe discret de transformations affines de son algèbre de Lie dont la partie linéaire est Zariski-dense dans et qui est libre, non abélien et agit proprement sur .
For any noncompact semisimple real Lie group , we construct a group of affine transformations of its Lie algebra whose linear part is Zariski-dense in and which is free, nonabelian and acts properly discontinuously on .
Révisé le : 2015-06-18
Accepté le : 2015-09-09
Publié le : 2016-02-16
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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