Poincare-Birkhoff-Witt Deformations of Calabi-Yau Algebras

Details Poincare-Birkhoff-Witt Deformations of Calabi-Yau Algebras Poincare-Birkhoff-Witt Deformations of Calabi-Yau Algebras

2006-10-03

arxiv.org/abs/math/0610112v2

Mathematics

Representation Theory

Minor errors corrected, results unchanged

Scientific paper

Recently, Bocklandt proved a conjecture by Van den Bergh in its graded version, stating that a graded quiver algebra (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.

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