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In this article, we investigate the representations of the Drinfeld doubles D(Rmn(q)) of the Radford Hopf algebras Rmn(q) over an algebraically closed field k, where m> 1 and n> 1 are integers and q∈kis a root of unity of order n. Under the assumption char(k)|╱mn, all the finite-dimensional indecomposable modules over D(Rmn(q)) are displayed and classified up to isomorphism. The Auslander-Reiten sequences in the category of finite-dimensional D(Rmn(q))-modules are also all displayed. It is shown that D(Rmn(q)) is of tame representation type.

Let H be a Hopf algebra in a rigid symmetric monoidal category C then the evaluation map τis a convolution-invertible skew pairing. In the previous paper, we constructed a Hopf algebra D(H)=H ⋈r H*cop in C. In this paper, we first show that D(H) is a quasitriangular Hopf algebra in C. Next, let H be an ordinary triangular finite-dimensional Hopf algebra. Then one can form quasitriangular Hopf algebras B(H,H) and B(H,D(H)) (in a rigid braided monoidal category) by Majid's method associated to the ordinary Hopf algebra maps H →H and iH H → D(H), where D(H) is the Drin-fePd quantum double. We show that D(B(H,H)) and B(H,D(H)) are isomorphic Hopf algebras in the braided monoidal category.