C^＊-Structure of Quantum Double for Finite Hopf C^＊-Algebra

Let H be a finite Hopf C*-algebra and H' be its dual Hopf algebra. Drinfeld's quantum double D(H) of H is a Hopf *-algebra. There is a faithful positive linear functional θ on D(H). Through the associated Gelfand-Naimark-Segal (GNS) representation, D(H) has a faithful *-representation so that it becomes a Hopf C*-algebra. The canonical embedding map of H into D(H) is isometric.