Poincaré-Birkhoff-Witt deformations of Calabi-Yau algebras

By R. Berger, R. Taillefer. 2006

70 citations recorded by the source corpus.

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 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/271b918eb13d63947689abae40fa1d1874af7b40

Citations in the corpus

• Superpotentials and higher order derivations (2008, unknown): “us relations of degree Nrather than two [4]). We recall that a graded algebra over a field kis AS-Gorenstein if Exti A(k,k) ∼= ( 0 i6= n k i= n It is clear by extending the proof of proposition 4.3 in [7] that graded twisted Calabi-Yau algebras over a field are AS-Gorenstein. In the other direction, t”