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

Abstract

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.

30 pages

References in corpus (2)

• Calabi-Yau algebras
• Calabi-Yau pointed Hopf algebras of finite Cartan type

Cited by in corpus (1)

• Skew Calabi-Yau Algebras and Homological Identities