Representations of the Drinfeld doubles of Pointed rank one Hopf algebras

Fuente: arXiv
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Auteurs principaux: Sun, Hua, Chen, Huixiang, Zhang, Yinhuo
Format: Preprint
Publié: 2025
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author Sun, Hua
Chen, Huixiang
Zhang, Yinhuo
author_facet Sun, Hua
Chen, Huixiang
Zhang, Yinhuo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_18216
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Representations of the Drinfeld doubles of Pointed rank one Hopf algebras
Sun, Hua
Chen, Huixiang
Zhang, Yinhuo
Quantum Algebra
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.
title Representations of the Drinfeld doubles of Pointed rank one Hopf algebras
topic Quantum Algebra
url https://arxiv.org/abs/2510.18216