Representation type of Frobenius-Lusztig kernels

TL;DR

This paper demonstrates that nearly all blocks of Frobenius-Lusztig kernels exhibit wild representation type, extending previous results, and confirms a conjecture about the infinite nature of Auslander-Reiten components in certain selfinjective algebras.

Contribution

It extends the classification of Frobenius-Lusztig kernels' blocks as wild and verifies a conjecture on the structure of Auslander-Reiten components in specific algebras.

Findings

Almost all blocks of Frobenius-Lusztig kernels are of wild representation type.

Confirmed the conjecture on infinitely many Auslander-Reiten components.

Extended previous results from the principal block to all blocks.

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.