Abstract: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.
Keywords: Hopf algebra, $2$-cocycle, braided Hopf algebra
AMS Subject Classification: 16W30