compact quantum group

Definition 0.1.

A compact quantum group, $Q_{C\mathit{}G}$ is defined as a particular case of a locally compact quantum group $Q_{LCG}$, that is, a quadruple $(A,\mathrm{\Delta },\mu ,\nu )$, where $A$ is either a $C^{*}$– or a $W^{*}$– algebra equipped with a co-associative comultiplication (http://planetmath.org/WeakHopfCAlgebra2) $\mathrm{\Delta }:A\to A\otimes A$, and two faithful semi-finite normal weights, $\mu$ and $\nu$ –right and -left Haar measures, and also when the object space $𝐎$ of the latter $Q_{LCG}$ is replaced by a compact topological space $Q_{CG}^T$, instead of being a locally compact topological space like $Q_{LCG}$.

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 group
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