It is a joint work with Rachel Taillefer. 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. Our main result is the following: if we add to W any potential of smaller degree, we get a Calabi-Yau algebra which is a Poincaré-Birkhoff-Witt (PBW) deformation of A, and the so-obtained PBW deformations are characterised among all the PBW deformations of A. This main result and some examples will be presented. An N-version of the PBW theorem due to Ginzburg and myself will be used.
- http://arxiv.org/abs/math.RT/0610112 - Our paper