Compact quantum groups and group duality
type: Item
instance of: scholarly article
title: Compact quantum groups and group duality
zbMATH Open document ID: 0755.17013
author: Xiu-Chi Quan
published in: Acta Applicandae Mathematicae
publication date: 1992-09-27T00:00:00Z
review text: The author studies compact quantum groups (roughly, Hopf \(C^*\)-algebras with unity) and shows that if the underlying \(C^*\)-algebra of a compact quantum group is commutative, then it is isomorphic to the algebra of functions on a compact group (a consequence of the Gelfand-Naimark theorem). He also gives versions of the preceding for compact quantum semigroups and locally compact quantum groups (roughly, Hopf \(C^*\)- algebras without unity, here multipliers are used). The topological dual of the \(C^*\)-algebra of a compact quantum group \(G\) is shown to be a Banach algebra, and the finite dimensional representations of \(G\) are representations of this dual algebra. [See also \textit{S. L. Woronowicz}, Commun. Math. Phys. 111, 613-665 (1987; Zbl 0627.58034)].
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 22D25
Mathematics Subject Classification ID: 46L89
zbMATH DE Number: 64119
zbMATH Keywords: compact quantum groups
zbMATH Keywords: Hopf \(C^*\)-algebras
zbMATH Keywords: compact quantum semigroups
zbMATH Keywords: locally compact quantum groups
zbMATH Keywords: topological dual
zbMATH Keywords: finite dimensional representations
reviewed by: Nicolás Andruskiewitsch
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 64119