Automorphism Group of Representation Ring of the Weak Hopf Algebra $$\widetilde{H_8 }$$H8∼

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