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.