2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77496Let k be a field and A a noetherian (noncommutative) k-algebra. The rigid dualizing complex of A was introduced by Van den Bergh. When A = U(g), the enveloping algebra of a finite dimensional Lie algebra g, Van den Bergh conjectured that the rigid dualizing complex is (U(g) \otimes \wedge^{n} g)[n], where n = dim g. We prove this conjecture, and give a few applications in representation theory and Hochschild cohomology.8 pages, AMSLaTeXRings and AlgebrasRepresentation Theory16D90; 16E40, 16E30, 17B55text