Auslander–Reiten theory of Frobenius–Lusztig kernels

In this paper, we show that the tree class of a component of the stable Auslander–Reiten quiver of a Frobenius–Lusztig kernel is one of the three infinite Dynkin diagrams. For the special case of the small quantum group, we show that the periodic components are homogeneous tubes and that the non-periodic components have shape $\mathbb{Z}[\mathbb{A}_\infty]$ if the component contains a module for the infinite-dimensional quantum group.