Article
| Title: | Automorphism group of green algebra of weak Hopf algebra corresponding to Sweedler Hopf algebra (English) |
| Author: | Cao, Liufeng |
| Author: | Su, Dong |
| Author: | Yao, Hua |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 101-115 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $r(\mathfrak {w}^0_2)$ be the Green ring of the weak Hopf algebra $\mathfrak {w}^0_2$ corresponding to Sweedler's 4-dimensional Hopf algebra $H_2$, and let ${\rm Aut}(R(\mathfrak {w}^0_2))$ be the automorphism group of the Green algebra $R(\mathfrak {w}^0_2)=r(\mathfrak {w}^0_2)\otimes _\mathbb {Z}\mathbb {C}$. We show that the quotient group ${\rm Aut}(R(\mathfrak {w}^0_2))/C_2\cong S_3$, where $C_2$ contains the identity map and is isomorphic to the infinite group $(\mathbb {C}^*,\times )$ and $S_3$ is the symmetric group of order 6. (English) |
| Keyword: | Green algebra |
| Keyword: | automorphism group |
| Keyword: | weak Hopf algebra |
| MSC: | 16W20 |
| MSC: | 19A22 |
| idZBL: | Zbl 07655757 |
| idMR: | MR4541091 |
| DOI: | 10.21136/CMJ.2022.0436-21 |
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| Date available: | 2023-02-03T11:08:29Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151506 |
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