Hopf algebras with the dual Chevalley property of discrete corepresentation type
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918224933683200 |
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| author | Yu, Jing Liu, Gongxiang |
| author_facet | Yu, Jing Liu, Gongxiang |
| contents | We try to classify Hopf algebras with the dual Chevalley property of discrete corepresentation type over an algebraically closed field $\Bbb{k}$ with characteristic 0. For such Hopf algebra $H$, we characterize the link quiver of $H$ and determine the structures of the link-indecomposable component $H_{(1)}$ containing $\Bbb{k}1$. Besides, we construct an infinite-dimensional non-pointed non-cosemisimple link-indecomposable Hopf algebra $H(e_{\pm 1}, f_{\pm 1}, u, v)$ with the dual Chevalley property of discrete corepresentation type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20292 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hopf algebras with the dual Chevalley property of discrete corepresentation type Yu, Jing Liu, Gongxiang Quantum Algebra Representation Theory 16T05, 16G60, 16G20, 16G10 We try to classify Hopf algebras with the dual Chevalley property of discrete corepresentation type over an algebraically closed field $\Bbb{k}$ with characteristic 0. For such Hopf algebra $H$, we characterize the link quiver of $H$ and determine the structures of the link-indecomposable component $H_{(1)}$ containing $\Bbb{k}1$. Besides, we construct an infinite-dimensional non-pointed non-cosemisimple link-indecomposable Hopf algebra $H(e_{\pm 1}, f_{\pm 1}, u, v)$ with the dual Chevalley property of discrete corepresentation type. |
| title | Hopf algebras with the dual Chevalley property of discrete corepresentation type |
| topic | Quantum Algebra Representation Theory 16T05, 16G60, 16G20, 16G10 |
| url | https://arxiv.org/abs/2409.20292 |