Grothendieck ring of quantum double of finite groups

Abstract

Let kG be a group algebra, and D(kG) its quantum double. We first prove that the structure of the Grothendieck ring of D(kG) can be induced from the Grothendieck ring of centralizers of representatives of conjugate classes of G. As a special case, we then give an application to the group algebra kD n , where k is a field of characteristic 2 and D n is a dihedral group of order 2n.