Taft algebra actions on preprojective algebras

TL;DR

This paper classifies how generalized Taft algebras act on preprojective algebras associated with extended Dynkin quivers of type A, extending known classifications and computing invariants in specific cases.

Contribution

It provides a classification of Taft algebra actions on preprojective algebras and computes invariants, linking group actions to algebra centers.

Findings

Classification of actions on preprojective algebras

Computation of invariants under Taft actions

Identification of invariant rings as algebra centers

Abstract

We classify actions of generalized Taft algebras on preprojective algebras of extended Dynkin quivers of type $A$. This may be viewed as an extension of the problem of classifying actions on the polynomial ring in two variables. In cases where the grouplike element acts via rotation on the underlying quiver, we compute invariants of the Taft action and, in certain cases, show that the invariant ring is isomorphic to the center of the preprojective algebra.