2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171135This survey paper is an exposition of old and recent results of Kostant and al. on the relationships between the exterior algebra of a simple Lie algebra and the action of the Casimir operator on it. Our exposition relies on u-cohomology and it is basically self-contained.Latex file, 11 pages, revised version. To appear in "Rendiconti di Matematica e delle sue Applicazioni"Representation Theorytext