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November 2011 On discontinuous subgroups acting on solvable homogeneous spaces
Ali Baklouti
Proc. Japan Acad. Ser. A Math. Sci. 87(9): 173-177 (November 2011). DOI: 10.3792/pjaa.87.173

Abstract

We present in this note an analogue of the Selberg-Weil-Kobayashi local rigidity Theorem in the setting of exponential Lie groups and substantiate two related conjectures. We also introduce the notion of stable discrete subgroups of a Lie group $G$ following the stability of an infinitesimal deformation introduced by T. Kobayashi and S. Nasrin (cf. [11]). For Heisenberg groups, stable discrete subgroups are either non-abelian or abelian and maximal. When $G$ is threadlike nilpotent, non-abelian discrete subgroups are stable. One major aftermath of the notion of stability as reveal some studied cases, is that the related deformation spaces are Hausdorff spaces and in most of the cases endowed with smooth manifold structures.

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Ali Baklouti. "On discontinuous subgroups acting on solvable homogeneous spaces." Proc. Japan Acad. Ser. A Math. Sci. 87 (9) 173 - 177, November 2011. https://doi.org/10.3792/pjaa.87.173

Information

Published: November 2011
First available in Project Euclid: 4 November 2011

zbMATH: 1241.22009
MathSciNet: MR2863361
Digital Object Identifier: 10.3792/pjaa.87.173

Subjects:
Primary: 22E27
Secondary: 32G05

Keywords: deformation space , discontinuous subgroup , proper action , rigidity , Solvable Lie subgroup , stability

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 9 • November 2011
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