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Let $H$ be a finite dimensional semisimple Hopf algebra and $R$ a braidedHopf algebra in the category of Yetter-Drinfeld modules over $H$. When $R$ is aCalabi-Yau algebra, a necessary and sufficient condition for $R#H$ to be aCalabi-Yau Hopf algebra is given. Conversely, when $H$ is the group algebra ofa finite group and the smash product $R#H$ is a Calabi-Yau algebra, we give anecessary and sufficient condition for the algebra $R$ to be a Calabi-Yaualgebra.

The Calabi-Yau property of Hopf algebras and braided Hopf algebras