Characterization of automorphisms of Radford's biproduct of Hopf group-coalgebra

Wang, Xing, Lu, Daowei, and Wang, Ding-Guo. "Characterization of automorphisms of Radford's biproduct of Hopf group-coalgebra." Czechoslovak Mathematical Journal 74.4 (2024): 1059-1082. <http://eudml.org/doc/299652>.

@article{Wang2024,
abstract = {We study certain subgroups of the Hopf group-coalgebra automorphism group of Radford’s $\pi $-biproduct. Firstly, we discuss the endomorphism monoid $\{\rm End\}_\{\pi \text\{-Hopf\}\}(A\times H, p)$ and the automorphism group $\{\rm Aut\}_\{\pi \text\{-Hopf\}\}(A\times H, p)$ of Radford’s $\pi $-biproduct $A \times H =\lbrace A \times H_\alpha \rbrace _\{\alpha \in \pi \}$, and prove that the automorphism has a factorization closely related to the factors $A$ and $H=\lbrace H_\alpha \rbrace _\{\alpha \in \pi \}$. What’s more interesting is that a pair of maps $(F_L,F_R)$ can be used to describe a family of mappings $F=\lbrace F_\alpha \rbrace _\{\alpha \in \pi \}$. 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.},
author = {Wang, Xing, Lu, Daowei, Wang, Ding-Guo},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hopf group-coalgebra; Radford’s $\pi $-biproduct; automorphism},
language = {eng},
number = {4},
pages = {1059-1082},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterization of automorphisms of Radford's biproduct of Hopf group-coalgebra},
url = {http://eudml.org/doc/299652},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Wang, Xing
AU - Lu, Daowei
AU - Wang, Ding-Guo
TI - Characterization of automorphisms of Radford's biproduct of Hopf group-coalgebra
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 4
SP - 1059
EP - 1082
AB - We study certain subgroups of the Hopf group-coalgebra automorphism group of Radford’s $\pi $-biproduct. Firstly, we discuss the endomorphism monoid ${\rm End}_{\pi \text{-Hopf}}(A\times H, p)$ and the automorphism group ${\rm Aut}_{\pi \text{-Hopf}}(A\times H, p)$ of Radford’s $\pi $-biproduct $A \times H =\lbrace A \times H_\alpha \rbrace _{\alpha \in \pi }$, and prove that the automorphism has a factorization closely related to the factors $A$ and $H=\lbrace H_\alpha \rbrace _{\alpha \in \pi }$. What’s more interesting is that a pair of maps $(F_L,F_R)$ can be used to describe a family of mappings $F=\lbrace F_\alpha \rbrace _{\alpha \in \pi }$. 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.
LA - eng
KW - Hopf group-coalgebra; Radford’s $\pi $-biproduct; automorphism
UR - http://eudml.org/doc/299652
ER -