Pairing and Quantum Double of Finite Hopf C*-Algebras

Abstract

This paper defines a pairing of two finite Hopf C*-algebras $A$ and $B$, and investigates the interactions between them. If the pairing is non-degenerate, then the quantum double construction is given. This construction yields a new finite Hopf C*-algebra $D(A,B)$. The canonical embedding maps of $A$ and $B$ into the double are both isometric.