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Automorphism group of green algebra of weak Hopf algebra corresponding to Sweedler Hopf algebra
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 101-115
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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 $R(\mathfrak {w}^0_2)=r(\mathfrak {w}^0_2)\otimes _\mathbb {Z}\mathbb {C}$. 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.
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 $R(\mathfrak {w}^0_2)=r(\mathfrak {w}^0_2)\otimes _\mathbb {Z}\mathbb {C}$. 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.
DOI : 10.21136/CMJ.2022.0436-21
Classification : 16W20, 19A22
Keywords: Green algebra; automorphism group; weak Hopf algebra 
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Cao, Liufeng; Su, Dong; Yao, Hua. Automorphism group of green algebra of weak Hopf algebra corresponding to Sweedler Hopf algebra. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 101-115. doi: 10.21136/CMJ.2022.0436-21

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