Geodesic
Characterization of automorphisms of Radford's biproduct of Hopf group-coalgebra
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1059-1082 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/CMJ.2024.0454-23
Classification : 16T05, 16U20
Keywords: Hopf group-coalgebra; Radford's $\pi $-biproduct; automorphism 
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     author = {Wang, Xing and Lu, Daowei and Wang, Ding-Guo},
     title = {Characterization of automorphisms of {Radford's} biproduct of {Hopf} group-coalgebra},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1059--1082},
     year = {2024},
     volume = {74},
     number = {4},
     doi = {10.21136/CMJ.2024.0454-23},
     language = {en},
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Wang, Xing; Lu, Daowei; Wang, Ding-Guo. Characterization of automorphisms of Radford's biproduct of Hopf group-coalgebra. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1059-1082. doi: 10.21136/CMJ.2024.0454-23

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