The Calabi-Yau property of smash products

Let H be a 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. (C) 2012 Elsevier Inc. All rights reserved.

Publication year:2012

Keywords:Calabi-Yau algebra, Braided Hopf algebra, Smash product, Mathematics

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Authors:International

Authors from:Higher Education

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