General Double Quantum Groups

Abstract

We introduce the concept of a twisted tensor biproduct, generalizing the general product given in Caenepeel et al. [1]. We give necessary and sufficient conditions for the new object to be a bialgebra and study the case of *-bialgebras. We describe all braided structures on the twisted tensor biproduct and introduce the notion of a general double quantum group. As an application, the special cases and examples are given.

Key Words:

• Braided Hopf algebra
• Braided monoidal category
• General double quantum group
• Twisted tensor biproduct

2000 Mathematics Subject Classification:

• 16W30

ACKNOWLEDGMENTS

The authors would like to thank the referee for his/her valuable comments on this article. This work was partially supported by the SRFDPHE (20060286006), the FNS of CHINA (10871042), and the EMSTRKF of China (108154).

Notes

Communicated by E. Puczylowski.