2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59558We give some examples of non-complete invariant affine connections on nilpotent and filiform Lie groups. This permits to describe non-nilpotent faithful representations on the model of filiform n-dimensional Lie algebras and, in particular, on the 3 dimensional Heisenberg algebra.6 pagesRings and AlgebrasDifferential GeometryRepresentation Theory17B30 ; 53B05text