Morita equivalence for weak Hopf–Galois extensions

ABSTRACT

Let H be a commutative weak Hopf algebra over a fixed field k, and A,B be weak H-Hopf Galois extensions. In this paper, we give a structure theorem for the category ${}_A{\mathcal{ℳ}}_B^H$ of weak relative Hopf bimodules. We also investigate the Morita equivalences between A and B based on the structure theorem.

KEYWORDS:

• Morita equivalence
• weak Hopf algebra
• weak Hopf–Galois extension
• weak relative Hopf bimodule

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16W30

Acknowledgment

The authors would like to thank the referee and Doctor Zhi Chen for their helpful suggestions and helps.