Automorphism Group of Representation Ring of the Weak Hopf Algebra H_8

Let H 8 be the unique noncommutative and noncocommutative eight dimensional semi-simple Hopf algebra. We first construct a weak Hopf algebra H_8 based on H 8 , then we investigate the structure of the representation ring of H_8 . Finally, we prove that the automorphism group of r( H_8 ) is just isomorphic to D 6 , where D 6 is the dihedral group with order 12.