Representations of Drinfeld doubles of Radford Hopf algebras

In this article, we investigate the representations of the Drinfeld doubles D(R_mn(q)) of the Radford Hopf algebras R_mn(q) over an algebraically closed field \(\mathbb{k}\) $$\mathbb{k}$$ , where m > 1 and n > 1 are integers and \(q \in \mathbb{k}\) $$q\in \mathbb{k}$$ is a root of unity of order n. Under the assumption \({\rm char}(\mathbb{k}) \ \Bigg\vert\!\!\!\diagup \ mn\) $$\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}(\mathbb{k})|╱mn$$ , all the finite-dimensional indecomposable modules over D(R_mn(q)) are displayed and classified up to isomorphism. The Auslander-Reiten sequences in the category of finite-dimensional D(R_mn(q))-modules are also all displayed. It is shown that D(R_mn(q)) is of tame representation type.