On the local rigidity of discontinuous groups for exponential solvable Lie groups
-
Ali Baklouti
and
Imed Kedim
Abstract.
Let H be an arbitrary closed connected subgroup of
an exponential solvable Lie group. Then a deformation of a
discontinuous subgroup Γ of G for the homogeneous
space G/H may be locally rigid. When G is nilpotent,
connected and simply connected, the question whether the Weil–Kobayashi
local rigidity fails to hold is posed by Baklouti [Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 9, 173–177]. A positive answer is only provided for some very few cases by now. This note aims to positively answer this question for some new settings. Our study goes even farther to exponential groups. In this case, the local rigidity fails to hold
if the automorphism group of the Lie algebra of the syndetic hull of Γ is not solvable. In addition,
any deformation of an abelian discontinuous subgroup is shown to be continuously deformable outside the setting of the affine group 
.
© 2013 by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- Geometric and harmonic analysis on homogeneous spaces and applications
- On the local rigidity of discontinuous groups for exponential solvable Lie groups
- La formule de Penney–Plancherel des restrictions à multiplicités finies des groupes de Lie nilpotents
- Invariant differential operators on the Heisenberg group and Meixner–Pollaczek polynomials
- Generalized Hermite expansions of functions arising from Hardy conditions
- The unitary representations parametrized by the Wallach set for a homogeneous bounded domain
Articles in the same Issue
- Masthead
- Geometric and harmonic analysis on homogeneous spaces and applications
- On the local rigidity of discontinuous groups for exponential solvable Lie groups
- La formule de Penney–Plancherel des restrictions à multiplicités finies des groupes de Lie nilpotents
- Invariant differential operators on the Heisenberg group and Meixner–Pollaczek polynomials
- Generalized Hermite expansions of functions arising from Hardy conditions
- The unitary representations parametrized by the Wallach set for a homogeneous bounded domain
