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Properly discontinuous group actions on affine homogeneous spaces

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Abstract

Let G be a real algebraic group, H ≤ G an algebraic subgroup containing a maximal reductive subgroup of G, and Γ a subgroup of G acting on G/H by left translations. We conjecture that Γ is virtually solvable provided its action on G/H is properly discontinuous and ΓG/H is compact, and we confirm this conjecture when G does not contain simple algebraic subgroups of rank ≥2. If the action of Γ on G/H (which is isomorphic to an affine linear space A n) is linear, our conjecture coincides with the Auslander conjecture. We prove the Auslander conjecture for n ≤ 5.

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Authors and Affiliations

  1. Institut Camille Jordan, Université Claude Bernard–Lyon 1, Bâtiment de Mathématiques, 43 Bld. du 11 Novembre 1918, 69622, Villeurbanne Cedex, France

    George Tomanov

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  1. George Tomanov
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Correspondence to George Tomanov.

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Dedicated to V.P. Platonov on the occasion of his 75th birthday

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Tomanov, G. Properly discontinuous group actions on affine homogeneous spaces. Proc. Steklov Inst. Math. 292, 260–271 (2016). https://doi.org/10.1134/S008154381601017X

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