Representations of the Drinfeld doubles of Pointed rank one Hopf algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917029357813760 |
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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 |