Pairing and Quantum Double of Finite Hopf C*-Algebras

2009/08/07 by Ming Liu, Liu, Ming, Li Ning Jiang +3
Mathematics · #16W30 #46K70 #81R05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16W30 #msc:46K70 #msc:81R05

paper · pdf · doi:10.48550/arxiv.0908.1046

10 pages,

arxiv created 2009/08/07 · openalex publication_date 2009/08/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• From subfactors to categories and topology II: The quantum double of tensor categories and subfactors

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• The Quantum Double of Hopf Algebras Realized via Partial Dualization and the Tensor Category of Its Representations
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