Representations of Finite Dimensional Pointed Hopf Algebras over $\mathbb{z}_n$

TL;DR

This paper investigates the representation theory of new finite-dimensional pointed Hopf algebras over cyclic groups in positive characteristic, revealing their symmetry, simple modules, and wild representation type.

Contribution

It provides a detailed classification of simple modules and projective covers for these Hopf algebras, and establishes their wild representation type, extending understanding of their structure.

Findings

Hopf algebras are symmetric algebras

Determined simple modules and projective covers

Proved these algebras are of wild representation type

Abstract

In this paper, we study the representations of the new finite-dimensional pointed Hopf algebras in positive characteristic given in \cite{Cib09}. We find that these Hopf algebras are symmetric algebras. We determine the simple modules and their projective covers over these Hopf algebras. We show that these Hopf algebras are of wild representation type.