An Isaac Newton Institute Workshop

Trends in Noncommutative Geometry

Poincaré-Birkhoff-Witt deformations of Calabi-Yau algebras

Authors: Roland BERGER (Saint-Etienne, France), Rachel TAILLEFER (Saint-Etienne, France)

Abstract

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.

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