Properly discontinuous group actions on affine homogeneous spaces

被引：0
作者：
George Tomanov
机构：
[1] Université Claude Bernard–Lyon 1,Institut Camille Jordan
[2] Bâtiment de Mathématiques,undefined
来源：
Proceedings of the Steklov Institute of Mathematics | 2016年 / 292卷
关键词：
STEKLOV Institute; Symmetric Space; Homogeneous Space; Algebraic Group; Linear Algebraic Group;
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摘要：
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 An) is linear, our conjecture coincides with the Auslander conjecture. We prove the Auslander conjecture for n ≤ 5.
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页码：260 / 271
页数：11
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