Proceedings of the Japan Academy, Series A, Mathematical Sciences

On discontinuous subgroups acting on solvable homogeneous spaces

Ali Baklouti

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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.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 9 (2011), 173-177.

First available in Project Euclid: 4 November 2011

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Zentralblatt MATH identifier

Primary: 22E27: Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
Secondary: 32G05: Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]

Solvable Lie subgroup proper action deformation space discontinuous subgroup rigidity stability


Baklouti, Ali. On discontinuous subgroups acting on solvable homogeneous spaces. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 9, 173--177. doi:10.3792/pjaa.87.173.

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