Constructing New Quasitriangular Turaev Group Coalgebras

Abstract

In this article, we construct a lot of new examples of Hopf group coalgebras by considering Majid's bicrossproduct Hopf algebra in Turaev category. Furthermore, we find the sufficient and necessary conditions for such Majid's bicrossproduct Hopf algebra to admit quasitriangular structures in the sense of Turaev group coalgebras.

Key Words:

• Majid's bicrossproduct Hopf algebra
• Quasitriangular Turaev group coalgebra
• Turaev category
• Turaev group coalgebra

2010 Mathematics Subject Classification:

• 16T05
• 16T15

ACKNOWLEDGMENTS

The authors would like to thank the referee for his/her valuable comments on this article. The work was partially supported by the NNSF of Jiangsu Province (No. BK2012736), the NSF of Henan Province (No. 102300410049) and the NNSF of China (No. 11101128).

Notes

Communicated by M. Cohen.