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April, 2008 Déformations de réseaux dans certains groupes résolubles
Cédric ROUSSEAU
J. Math. Soc. Japan 60(2): 397-421 (April, 2008). DOI: 10.2969/jmsj/06020397

Abstract

We aim to study local rigidity and deformations for the following class of groups: the semidirect product Γ= Z n A Z where n2 is an integer and A is a hyperbolic matrix in SL( n,Z ) , considered first as a lattice in the solvable Lie group G= R n A R , then as a subgroup of the semisimple Lie group SL( n+1,R ) . We will notably show that, although Γ 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 Γ in G is conjugated to Γ by an element of SL( n+1,R ) .

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Cédric ROUSSEAU. "Déformations de réseaux dans certains groupes résolubles." J. Math. Soc. Japan 60 (2) 397 - 421, April, 2008. https://doi.org/10.2969/jmsj/06020397

Information

Published: April, 2008
First available in Project Euclid: 30 May 2008

zbMATH: 1144.22009
Digital Object Identifier: 10.2969/jmsj/06020397

Subjects:
Primary: 22E25 , 22E40

Keywords: Group cohomology , lattices in solvable Lie groups , local rigidity

Rights: Copyright © 2008 Mathematical Society of Japan

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Vol.60 • No. 2 • April, 2008
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