Coradically graded Hopf algebras with the dual Chevalley property of tame corepresentation type
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909274946404352 |
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| author | Yu, Jing Liu, Gongxiang |
| author_facet | Yu, Jing Liu, Gongxiang |
| contents | Let $\Bbbk$ be an algebraically closed field of characteristic 0 and $H$ a finite-dimensional Hopf algebra over $\Bbbk$ with the dual Chevalley property. In this paper, we show that $\operatorname{gr}^c(H)$ is of tame corepresentation type if and only if $\operatorname{gr}^c(H)\cong (\Bbbk\langle x,y\rangle/I)^* \times H^\prime$ for some finite-dimensional semisimple Hopf algebra $H^\prime$ and some special ideals $I$. Then, by the method of link quiver and bosonization, we discuss which of the above ideals will occur when $(\Bbbk\langle x,y\rangle/I)^* \times H_0$ is a Hopf algebra of tame corepresentation type under some assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coradically graded Hopf algebras with the dual Chevalley property of tame corepresentation type Yu, Jing Liu, Gongxiang Quantum Algebra Rings and Algebras Representation Theory 16T05, 16G60 (primary), 16G20, 16G10 (secondary) Let $\Bbbk$ be an algebraically closed field of characteristic 0 and $H$ a finite-dimensional Hopf algebra over $\Bbbk$ with the dual Chevalley property. In this paper, we show that $\operatorname{gr}^c(H)$ is of tame corepresentation type if and only if $\operatorname{gr}^c(H)\cong (\Bbbk\langle x,y\rangle/I)^* \times H^\prime$ for some finite-dimensional semisimple Hopf algebra $H^\prime$ and some special ideals $I$. Then, by the method of link quiver and bosonization, we discuss which of the above ideals will occur when $(\Bbbk\langle x,y\rangle/I)^* \times H_0$ is a Hopf algebra of tame corepresentation type under some assumptions. |
| title | Coradically graded Hopf algebras with the dual Chevalley property of tame corepresentation type |
| topic | Quantum Algebra Rings and Algebras Representation Theory 16T05, 16G60 (primary), 16G20, 16G10 (secondary) |
| url | https://arxiv.org/abs/2407.21389 |