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.

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DOI : 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
Mot 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
Smilga, Ilia 1

1 Department of Mathematics Yale University P.O. Box 208283 New Haven, CT 06520-8283 (USA)
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.3026/

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