Hopf algebras with the dual Chevalley property of finite corepresentation type

Abstract

Let $H$ be a finite-dimensional Hopf algebra over an algebraically closed field $\mathbb{k}$ 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 $\mathbb{k}1$ is a pointed Hopf algebra and the link quiver of $H_{(1)}$ is a basic cycle.