compact quantum group

Definition 0.1.

A compact quantum group, QCG is defined as a particular case of a locally compact quantum groupPlanetmathPlanetmath QLCG, that is, a quadruple (A,Δ,μ,ν), where A is either a C*– or a W*algebraPlanetmathPlanetmathPlanetmath equipped with a co-associative comultiplication ( Δ:AAA, and two faithfulPlanetmathPlanetmath semi-finite normal weights, μ and ν –right and -left Haar measures, and also when the object space 𝐎 of the latter QLCG is replaced by a compact topological space QCGT, instead of being a locally compact topological space like QLCG.


  • 1 A. Maes, and A. VanDaele. 1998. on Compact Quantum Groups.,, 43 pp.
Title compact quantum group
Canonical name CompactQuantumGroup
Date of creation 2013-03-22 18:24:07
Last modified on 2013-03-22 18:24:07
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 25
Author bci1 (20947)
Entry type Definition
Classification msc 81R15
Classification msc 81R50
Classification msc 46L05
Synonym quantum groupPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath
Synonym compact matrix quantum group
Related topic CAlgebra3
Related topic QuantumOperatorAlgebrasInQuantumFieldTheories
Related topic FiniteQuantumGroup
Related topic DualityInMathematics
Related topic LocallyCompactQuantumGroup
Related topic QuantumGroups
Related topic GelfandTransform