On discontinuous subgroups acting on solvable homogeneous spaces

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Ali Baklouti¹ 

[1] Department of Mathematics, University of Sfax, Faculty of Sciences at Sfax

关键词: Solvable Lie subgroup;    proper action;    deformation space;    discontinuous subgroup;    rigidity;    stability.;   

DOI  :  10.3792/pjaa.87.173

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

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.

【 授权许可】

Unknown