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 \(\Bbbk \) 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 \(\textrm{Q}(H)\) of H is a disjoint union of basic cycles, if and only if the link-indecomposable component \(H_{(1)}\) containing \(\Bbbk 1\) is a pointed Hopf algebra and the link quiver of \(H_{(1)}\) is a basic cycle.