JournalsjncgVol. 1, No. 2pp. 241–270

Poincaré–Birkhoff–Witt deformations of Calabi–Yau algebras

  • Roland Berger

    Université de Saint-Etienne
  • Rachel Taillefer

    Université de Saint-Etienne
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Abstract

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.

Cite this article

Roland Berger, Rachel Taillefer, Poincaré–Birkhoff–Witt deformations of Calabi–Yau algebras. J. Noncommut. Geom. 1 (2007), no. 2, pp. 241–270

DOI 10.4171/JNCG/6