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 $\mathbb{k}$, where $m>1$ and $n>1$ are integers and $q\in \mathbb{k}$ is a root of unity of order $n$. Under the assumption $\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}(\mathbb{k})\nmid mn$, 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.