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Abstract
Let X and A be weak Hopf algebras in the sense of Li (Citation1998). As in the case of Hopf algebras (Majid, Citation1990), a weak bicrossed coproduct X∞ R A is constructed by means of good regular R-matrices of the weak Hopf algebras X and A. Using this, we provide a new framework of obtaining singular solutions of the quantum Yang–Baxter equation by constructing weak quasitriangular structures over X∞ R A when both X and A admit a weak quasitriangular structure. Finally, two explicit examples are given.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The author would like to thank the referee for his/her valuable comments on this article. The author would like to thank Prof. Fang Li for sending me his articles and helpful discussions about this topic. This work was partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education (20060286006), the FNS of CHINA (10571026), and the Southeast University Fund (XJ0707273).
Notes
Communicated by E. I. Zelmanov.