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arXiv · 2510.18216

Representations of the Drinfeld doubles of Pointed rank one Hopf algebras

Hua Sun·Huixiang Chen·Yinhuo Zhang
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Abstract

In this paper, we investigate the representations of the Drinfeld doubles $D(H_{\mathcal{D}})$ of pointed rank one Hopf algebras $H_{\mathcal{D}}$ over an algebraically closed field $\Bbbk$ of characteristic zero. We provide a complete classification of all finite-dimensional indecomposable $D(H_{\mathcal{D}})$-modules up to isomorphism and explicitly describe the Auslander-Reiten sequences in the category of finite-dimensional $D(H_{\mathcal{D}})$-modules. We show that $D(H_{\mathcal{D}})$ is of tame representation type.

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BibTeXRIS

Hua Sun, Huixiang Chen, Yinhuo Zhang. 2025-10-21. Representations of the Drinfeld doubles of Pointed rank one Hopf algebras. https://arxiv.org/abs/2510.18216

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