Journal of the Mathematical Society of Japan

Déformations de réseaux dans certains groupes résolubles

Cédric ROUSSEAU

Full-text: Open access

Abstract

We aim to study local rigidity and deformations for the following class of groups: the semidirect product $\Gamma=\bm{Z}^{n}\rtimes_{A}\bm{Z}$  where $n\geq 2$  is an integer and $A$  is a hyperbolic matrix in $\SL{n}{Z}$, considered first as a lattice in the solvable Lie group $G=\bm{R}^{n}\rtimes_{A}\bm{R}$, then as a subgroup of the semisimple Lie group $\SL{n+1}{R}$. We will notably show that, although $\Gamma$  is locally rigid neither in $G$  nor in $H$, it is locally $\SL{n+1}{R}$-rigid in $G$  in the sense that every small enough deformation of $\Gamma$  in $G$  is conjugated to $\Gamma$  by an element of $\SL{n+1}{R}$.

Article information

Source
J. Math. Soc. Japan Volume 60, Number 2 (2008), 397-421.

Dates
First available in Project Euclid: 30 May 2008

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1212156656

Digital Object Identifier
doi:10.2969/jmsj/06020397

Zentralblatt MATH identifier
1144.22009

Subjects
Primary: 22E25: Nilpotent and solvable Lie groups 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]

Keywords
local rigidity lattices in solvable Lie groups group cohomology

Citation

ROUSSEAU, Cédric. Déformations de réseaux dans certains groupes résolubles. Journal of the Mathematical Society of Japan 60 (2008), no. 2, 397--421. doi:10.2969/jmsj/06020397. http://projecteuclid.org/euclid.jmsj/1212156656.


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