2008 年 60 巻 2 号 p. 397-421
We aim to study local rigidity and deformations for the following class of groups: the semidirect product Γ = Zn $\ times$A Z where n ≥ 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 = Rn $\ times$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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