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

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

2011-11-17

arxiv.org/abs/1111.4201v1

Mathematics

Quantum Algebra

30 pages

Scientific paper

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

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