Hopf algebras with the dual Chevalley property of finite corepresentation type

TL;DR

This paper characterizes finite-dimensional Hopf algebras with the dual Chevalley property that have finite corepresentation type, linking algebraic structure to quiver properties and pointedness.

Contribution

It provides a complete characterization of such Hopf algebras via their link quivers and pointedness, extending understanding of their structure.

Findings

H is of finite corepresentation type iff it is coNakayama.

H is of finite corepresentation type iff its link quiver is a disjoint union of basic cycles.

The link-indecomposable component containing the identity is a pointed Hopf algebra with a basic cycle link quiver.

Abstract

Let $H$ be a finite-dimensional Hopf algebra over an algebraically closed field $\Bbbk$ with the dual Chevalley property. We prove that $H$ is of finite corepresentation type if and only if it is coNakayama, if and only if the link quiver $\mathrm{Q}(H)$ of $H$ is a disjoint union of basic cycles, if and only if the link-indecomposable component $H_{(1)}$ containing $\Bbbk1$ is a pointed Hopf algebra and the link quiver of $H_{(1)}$ is a basic cycle.