Representation type of Frobenius-Lusztig kernels

Abstract

In this article we show that almost all blocks of all Frobenius-Lusztig kernels are of wild representation type extending results of Feldvoss andWitherspoon, who proved this result for the principal block of the zeroth Frobenius-Lusztig kernel. Furthermore we verify the conjecture that there are infinitely many Auslander-Reiten components for a finite dimensional algebra of infinite representation type for selfinjective algebras whose cohomology satisfies certain finiteness conditions.