# Article

Full entry | PDF   (0.2 MB)
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

Partner of