We aim to study local rigidity and deformations for the following class of groups: the semidirect product where is an integer and is a hyperbolic matrix in , considered first as a lattice in the solvable Lie group , then as a subgroup of the semisimple Lie group . We will notably show that, although is locally rigid neither in nor in , it is locally -rigid in in the sense that every small enough deformation of in is conjugated to by an element of .
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