Article
| Title: | Characterization of automorphisms of Radford's biproduct of Hopf group-coalgebra (English) |
| Author: | Wang, Xing |
| Author: | Lu, Daowei |
| Author: | Wang, Ding-Guo |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 4 |
| Year: | 2024 |
| Pages: | 1059-1082 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study certain subgroups of the Hopf group-coalgebra automorphism group of Radford's $\pi $-biproduct. Firstly, we discuss the endomorphism monoid ${\rm End}_{\pi \text {-Hopf}}(A\times \nobreak H, p)$ and the automorphism group ${\rm Aut}_{\pi \text {-Hopf}}(A\times H, p)$ of Radford's $\pi $-biproduct $A \times H =\{A \times H_\alpha \}_{\alpha \in \pi }$, and prove that the automorphism has a factorization closely related to the factors $A$ and $H=\{H_\alpha \}_{\alpha \in \pi }$. What's more interesting is that a pair of maps $(F_L,F_R)$ can be used to describe a family of mappings $F=\{F_\alpha \}_{\alpha \in \pi }$. Secondly, we consider the relationship between the automorphism group ${\rm Aut}_{\pi \text {-Hopf}}(A\times H, p)$ and the automorphism group ${\rm Aut}_{\pi \text {-}\mathcal {Y}\mathcal {D}\text {-Hopf}}(A)$ of $A$, and a normal subgroup of the automorphism group ${\rm Aut}_{\pi \text {-Hopf}}(A\times H, p)$. Finally, we specifically describe the automorphism group of an example. (English) |
| Keyword: | Hopf group-coalgebra |
| Keyword: | Radford's $\pi $-biproduct |
| Keyword: | automorphism |
| MSC: | 16T05 |
| MSC: | 16U20 |
| DOI: | 10.21136/CMJ.2024.0454-23 |
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| Date available: | 2024-12-15T06:35:33Z |
| Last updated: | 2024-12-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152689 |
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