compact quantum groupCompactQuantumGroup2008-09-19 23:36:002009-06-03 03:43:18Definitionquantum operator algebras in quantum field theoriescompact quantum groupLocallyCompactQuantumGroupC*-algebracompact matrix quantum groupquantum group % this is the default PlanetMath preamble. as your knowledge
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\newcommand{\hr}{{\hookrightarrow}}\begin{definition}
A \emph{compact quantum group, $Q_{CG}$} is defined as a particular case of a locally compact quantum group $Q_{LCG}$, that is, a quadruple $(A, \Delta, \mu, \nu)$, where $A$ is either a $C^*$-- or a
\PMlinkname{$W^*$-- algebra equipped with a co-associative comultiplication}{WeakHopfCAlgebra2}
$\Delta: A \to A \otimes A$, and two faithful semi-finite normal weights, $\mu$ and $\nu$ --right and -left Haar measures, and also when the object space $\mathbf{O}$ of the latter $Q_{LCG}$ is replaced by a compact topological space $Q^T_{CG}$, instead of being a locally compact topological space like $Q_{LCG}$.
\end{definition}
\begin{thebibliography}{9}
\bibitem{M-V98}
A. Maes, and A. VanDaele. 1998.
\PMlinkexternal{Notes on Compact Quantum Groups.}{http://arxiv.org/PS_cache/math/pdf/9803/9803122v1.pdf}, $arxiv.org.math-FA-9803122v1$, 43 pp.
\end{thebibliography}