Abstract
The Calabi–Yau property of the Poincare–Birkhoff–Witt deformation of a Koszul Calabi–Yau algebra is characterized. Berger and Taillefer (J Noncommut Geom 1:241–270, 2007, Theorem 3.6) proved that the Poincare–Birkhoff–Witt deformation of a Calabi–Yau algebra of dimension 3 is Calabi–Yau under some conditions. The main result in this paper generalizes their result to higher dimensional Koszul Calabi–Yau algebras. As corollaries, the necessary and sufficient condition obtained by He et al. (J Algebra 324:1921–1939, 2010) for the universal enveloping algebra, respectively, Sridharan enveloping algebra, of a finite-dimensional Lie algebra to be Calabi–Yau, is derived.
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