Proper affine actions on semisimple Lie algebras

Smilga, Ilia

doi:10.5802/aif.3026

Smilga, Ilia

Annales de l'Institut Fourier, Volume 66 (2016) no. 2, p. 785-831

Abstract
Résumé

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 $Ad G$ and which is free, nonabelian and acts properly discontinuously on $𝔤$ .

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 $Ad G$ et qui est libre, non abélien et agit proprement sur $𝔤$ .

Received : 2014-06-19
Revised : 2015-06-19
Accepted : 2015-09-10
Published online : 2016-02-17
DOI : https://doi.org/10.5802/aif.3026
Classification: 20G20, 22E40, 20H15
Keywords: Discrete subgroups of Lie groups, Affine groups, Auslander conjecture, Milnor conjecture, Flat affine manifolds, Adjoint representation, Margulis invariant, Quasi-translation, Free group, Schottky group

@article{AIF_2016__66_2_785_0,
     author = {Smilga, Ilia},
     title = {Proper affine actions on semisimple Lie algebras},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {2},
     year = {2016},
     pages = {785-831},
     doi = {10.5802/aif.3026},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2016__66_2_785_0}
}

Smilga, Ilia. Proper affine actions on semisimple Lie algebras. Annales de l'Institut Fourier, Volume 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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