Article
Keywords:
Hopf algebra; $2$-cocycle; braided Hopf algebra
Summary:
In this paper, we study the $H^{\sigma-R}$ type Hopf algebras and present its braided and quasitriangular Hopf algebra structure. This generalizes well-known results on $H^{\sigma }$ and $H^R$ type Hopf algebras. Finally, the classification of $H^{\sigma -R}$ type Hopf algebras is given.
References:
                        
[1] Doi Y.: 
Braided bialgebras and quadratic bialgebras. Comm. Algebra 21 (5) (1993), 1731-1749. 
MR 1213985 | 
Zbl 0779.16015[2] Doi Y., Takeuchi M.: 
Multiplication alteration by two-cocycles-The quantum version. Comm. Algebra 22 (14) (1994), 5715-5732. 
MR 1298746 | 
Zbl 0821.16038[3] Sweelder M.E.: 
Hopf Algebras. W.A. Benjamin, New York, 1969. 
MR 0252485[4] Majid S.: 
Quasitriangular Hopf Algebras and Yang-Baxter equations. Int. J. Modern Phys. A5 (1990), 1-91. 
MR 1027945 | 
Zbl 0709.17009[5] Montgomery S.: 
Hopf Algebras and Their Actions on Rings. CBMS 82, Amer. Math. Soc., 1993. 
MR 1243637 | 
Zbl 0793.16029[6] Radford D.E.: 
On the Quasitriangular structure of a semisimple Hopf Algebras. J. Algebra 141 (2) (1991), 354-358. 
MR 1125700[7] I-Peng Lin B.: 
Crossed coproducts of Hopf algebras. Comm. Algebra 10 (1) (1982), 1-17. 
MR 0674686[8] Reshetikhin N.Y.: 
Multiparameter quantum groups and twisted quasi-triangular Hopf algebras. Lett. Math. Phys. 20 (1990), 331-335. 
MR 1077966