Proper affine actions on semisimple Lie algebras

Smilga, Ilia

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 $𝔤$.

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

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