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Keywords:
automorphism group; representation ring; weak Hopf algebra
Summary:
Let $H_8$ be the unique noncommutative and noncocommutative eight dimensional semi-simple Hopf algebra. We first construct a weak Hopf algebra $\widetilde {H_8}$ based on $H_8$, then we investigate the structure of the representation ring of $\widetilde {H_8}$. Finally, we prove that the automorphism group of $r(\widetilde {H_8})$ is just isomorphic to $D_6$, where $D_6$ is the dihedral group with order 12.
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