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 $Q_{LCG}$.