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Keywords:
Green algebra; automorphism group; weak Hopf algebra
Green algebra; automorphism group; weak Hopf algebra
Summary:
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.
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