Journal of the Mathematical Society of Japan

Déformations de réseaux dans certains groupes résolubles


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

First available in Project Euclid: 30 May 2008

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Zentralblatt MATH identifier

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

local rigidity lattices in solvable Lie groups group cohomology


ROUSSEAU, Cédric. Déformations de réseaux dans certains groupes résolubles. J. Math. Soc. Japan 60 (2008), no. 2, 397--421. doi:10.2969/jmsj/06020397.

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