We study the Calabi–Yau property of pointed Hopf algebra of finite Cartan type. It turns out that this class of pointed Hopf algebras constructed by N. Andruskiewitsch and H.-J. Schneider contains many Calabi–Yau Hopf algebras. To give concrete examples of new Calab–Yau Hopf algebras, we classify the Calabi–Yau pointed Hopf algebras of dimension less than 5.
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Xiaolan Yu, Yinhuo Zhang, Calabi-Yau pointed Hopf algebras of finite Cartan type. J. Noncommut. Geom. 7 (2013), no. 4, pp. 1105–1144DOI 10.4171/JNCG/144