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

2011/11/17 by Xiaolan Yu, Yu, Xiaolan, Yinhuo Zhang +1
Mathematics · Physics and Astronomy · #16E40 #16S40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1111.4201

openalex publication_date 2011/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Calabi-Yau pointed Hopf algebras of finite Cartan type

Related

• Cocommutative Calabi-Yau Hopf algebras and deformations
• Calabi-Yau property under monoidal Morita-Takeuchi equivalence
• Yetter-Drinfeld categories for quasi-Hopf algebras
• Calabi-Yau pointed Hopf algebras of finite Cartan type
• On Lie Algebras in the Category of Yetter-Drinfeld Modules