Pairing and Quantum Double of Finite Hopf C*-Algebras

• DOI: 10.1007/s10114-005-0886-9
• Publication Date: 2006-12-07T19:22:27Z
• Authors: Ming Liu; Li Ning Jiang; Guo Sheng Zhang
• Keywords: Mathematics - Quantum Algebra; FOS: Mathematics; Quantum Algebra (math.QA); 0101 mathematics; 16W30; 46K70; 46K70;16W30;81R05; 01 natural sciences; 81R05

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.<br/>10 pages,<br/>