The Structure Theorem of Weak Comodule Algebras

Abstract

This article mainly gives the structure theorem of weak comodule algebras, that is, assume that H is a weak Hopf algebra, and B a weak right H-comodule algebra, if there exists a morphism φ: H → B of a weak right H-comodule algebras, then there exists an algebra isomorphism: B ≅ B ^coH #H, where B ^coH denotes the coinvariant subalgebra of B, and B ^coH #H denotes the weak smash product.

Key Words:

• Weak comodule algebras
• Weak Hopf algebras
• Weak Hopf bimodules
• Weak smash products

2000 Mathematics Subject Classification:

• 16W30

ACKNOWLEDGMENTS

The author would like to thank the referee for his/her careful reading of this article and helpful comments. This work was partly done during the author's visit at Ciudad University, Argentina, and is supported by Educational Ministry Science Technique Key Foundation of China (108154) and National Natural Science Foundation of China (10871170).

Notes

Communicated by K. Misra.