The Duality Theorem for Weak Hopf Algebra (Co) Actions

Abstract

In this article, we mainly study a new notion of a generalized smash product for weak Hopf comodule algebras and provide a new version of the duality theorem for weak smash products as an application.

Key Words:

• Duality theorem
• Quantum groupoids
• Weak (co)module algebras
• Weak generalized smash products
• Weak Hopf Galois extensions

2000 Mathematics Subject Classification:

• 16W30

ACKNOWLEDGMENTS

The authors would like to thank the referee for his/her very valuable comments. We are also grateful to Dr. Bingliang Shen and Dr. ling Liu for their discussions about Section 2. The work was partially supported by the NSF of China (No. 10871042), the NSF of Jiangsu Province (No. BK2009258), and the EMSTRKF of China (No. 108154).

Notes

Communicated by J. Alev.