Recently, Bocklandt proved a conjecture by Van den Bergh in its graded version, stating that a graded quiver algebra A (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 Poincaré–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.
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Roland Berger, Rachel Taillefer, Poincaré–Birkhoff–Witt deformations of Calabi–Yau algebras. J. Noncommut. Geom. 1 (2007), no. 2, pp. 241–270DOI 10.4171/JNCG/6