Proceedings of the Japan Academy, Series A, Mathematical Sciences
- Proc. Japan Acad. Ser. A Math. Sci.
- Volume 87, Number 9 (2011), 173-177.
On discontinuous subgroups acting on solvable homogeneous spaces
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. ). 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.
Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 9 (2011), 173-177.
First available in Project Euclid: 4 November 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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]
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. https://projecteuclid.org/euclid.pja/1320417396