2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103655We show that a solvable real rigid Lie algebra is not completelt rigid, by constructing an example of minimal dimension where the external torus is not spanned by $ad$-semisimple derivations over $\mathbb{R}$. We analyze the real forms of nilradicals of solvable rigid Lie algebras in dimensions $n\leq 7$ and give the real classification for dimension 8.8 pages, text in frenchRepresentation Theory17B30, 17B56text