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We study the Calabi-Yau property of pointed Hopf algebra U(D,λ) 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 Calabi-Yau Hopf algebras, we classify the Calabi-Yau pointed Hopf algebras U(D,λ) of dimension less than 5. © European Mathematical Society.

Calabi-Yau pointed Hopf algebras of finite Cartan type