Pairing and Quantum Double of Finite Hopf C*-Algebras

TL;DR

This paper introduces a pairing concept for finite Hopf C*-algebras, explores their interactions, and constructs a quantum double that results in a new finite Hopf C*-algebra with isometric embeddings.

Contribution

It defines a pairing for finite Hopf C*-algebras and constructs the quantum double, providing a new algebraic structure with isometric embeddings.

Findings

Quantum double construction yields a new finite Hopf C*-algebra

Embeddings of A and B into the double are isometric

Non-degenerate pairing is key to the construction

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.