Poincare-Birkhoff-Witt Deformations of Calabi-Yau Algebras

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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.
Minor errors corrected, results unchanged

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Representation Theory, Quantum Algebra, Rings and Algebras, 16E65, 16S38, 16S80

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http://salesiana.dossiersoluciones.com/handle/123456789/117810

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610112
 http://arxiv.org/abs/math/0610112

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arXiv