Czechoslovak Mathematical Journal, Vol. 73, No. 1, pp. 101-115, 2023
Automorphism group of green algebra of weak Hopf algebra corresponding to Sweedler Hopf algebra
Liufeng Cao, Dong Su, Hua Yao
Received November 23, 2021. Published online September 29, 2022.
Abstract: 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 $R(\mathfrak{w}^0_2)=r(\mathfrak{w}^0_2)øtimes_\mathbb{Z}\mathbb{C}$. 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.
Keywords: Green algebra; automorphism group; weak Hopf algebra
Affiliations: Liufeng Cao (corresponding author), School of Mathematical Sciences, Yangzhou University, Yangzhou, Jiangsu 225002, P. R. China, e-mail: 1204719495@qq.com; Dong Su, School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan 471023, P. R. China, e-mail: sudong@haust.edu.cn; Hua Yao, School of Mathematics and Statistics, Huanghuai University, Zhumadian, Henan 463000, P. R. China, e-mail: dalarston@126.com
