Proper affine actions on semisimple Lie algebras
Annales de l'Institut Fourier, Volume 66 (2016) no. 2, p. 785-831

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.

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.

Received : 2014-06-19
Revised : 2015-06-19
Accepted : 2015-09-10
Published online : 2016-02-17
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
     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 = {}
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.

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