Czechoslovak Mathematical Journal, first online, pp. 1-15


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
Classification MSC:  16W20, 19A22
DOI:  10.21136/CMJ.2022.0436-21

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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


 
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