JournalsjncgVol. 1 , No. 2DOI 10.4171/jncg/6

Poincaré–Birkhoff–Witt deformations of Calabi–Yau algebras

  • Roland Berger

    Université de Saint-Etienne
  • Rachel Taillefer

    Université de Saint-Etienne
Poincaré–Birkhoff–Witt deformations of Calabi–Yau algebras cover

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.