2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/117810Recently, Bocklandt proved a conjecture by Van den Bergh in its graded version, stating that a graded quiver algebra (with relations) which is Calabi-Yau of dimension 3 is defined from a homogeneous potential W. In this paper, we prove that if we add to W any potential of smaller degree, we get a Poincare-Birkhoff-Witt deformation of A. Such PBW deformations are Calabi-Yau and are characterised among all the PBW deformations of A. Various examples are presented.Minor errors corrected, results unchangedRepresentation TheoryQuantum AlgebraRings and Algebras16E65, 16S38, 16S80text