Automorphism Group of Representation Ring of the Weak Hopf Algebra $$\widetilde{H_8 }$$

Let H₈ be the unique noncommutative and noncocommutative eight dimensional semi-simple Hopf algebra. We first construct a weak Hopf algebra \(\widetilde{H_8 }\)based on H₈, then we investigate the structure of the representation ring of \(\widetilde{H_8 }\). Finally, we prove that the automorphism group of \(r\left( {\widetilde{H_8 }} \right)\)is just isomorphic to D₆, where D₆ is the dihedral group with order 12.