Derived discrete Hopf algebras with the Chevalley property

TL;DR

This paper classifies certain finite-dimensional Hopf algebras with the Chevalley property based on their derived representation type, identifying specific isomorphisms and describing their derived categories.

Contribution

It provides a complete classification of derived discrete Hopf algebras with the Chevalley property, identifying them with a specific algebraic structure and describing their derived categories.

Findings

Finite-dimensional indecomposable non-semisimple Hopf algebras with the Chevalley property are derived discrete iff isomorphic to (A(n, 2, μ, -1))^*.

Descriptions of indecomposable objects in the derived category of these algebras.

Determination of tensor products of indecomposable objects.

Abstract

We try to classify Hopf algebras with the Chevalley property according to their derived representation type. We show that a finite-dimensional indecomposable non-semisimple Hopf algebra $H$ with the Chevalley property is derived discrete if and only if it is isomorphic to $(A(n, 2, \mu, -1))^*$. Besides, we give a description for the indecomposable objects in $\mathcal{D}^b((A(n, 2, \mu, -1))^*)$ and determine their tensor products.