2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64818We prove the existence of a local smooth Levi decomposition for smooth Poisson structures and Lie algebroids near a singular point. In the appendix of this paper, we show an abstract Nash-Moser normal form theorem, which generalizes our Levi decomposition result and which may be helpful in the study of other smooth normal form problems.38 pages. The proof of the main theorem is simplified. An appendix about an abstract Nash-Moser normal form theorem is addedDifferential GeometrySymplectic Geometry53D17, 32S65text