Talk:PlanetPhysics/Representation of a CcG Topological Algebra

Original TeX Content from PlanetPhysics Archive

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%%% Primary Title: representation of a Cc(G)*- topological algebra
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%%% Filename: RepresentationOfACcGTopologicalAlgebra.tex
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%%% Owner: bci1
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\begin{document}

 \begin{definition}
A \emph{\htmladdnormallink{representation}{http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html} of a \htmladdnormallink{$C_c(\grp)$}{http://planetphysics.us/encyclopedia/C_cG.html} \htmladdnormallink{topological}{http://planetphysics.us/encyclopedia/CoIntersections.html} $*$--algebra} is defined as a \emph{continuous $*$--morphism from $C_c(\grp)$ to $B(\H)$, where $\grp$ is a \htmladdnormallink{topological groupoid}{http://planetphysics.us/encyclopedia/GroupoidHomomorphism2.html}, (usually a \htmladdnormallink{locally compact groupoid}{http://planetphysics.us/encyclopedia/LocallyCompactGroupoid.html}, $\grp_{lc}$), $\H $ is a \htmladdnormallink{Hilbert space}}{http://planetphysics.us/encyclopedia/NormInducedByInnerProduct.html}, and $B(\H)$ is the $C^*$-algebra of bounded \htmladdnormallink{linear operators}{http://planetphysics.us/encyclopedia/Commutator.html} on the Hilbert space $\H$; of course, one considers the inductive limit (strong) topology to be defined on $C_c(\grp)$,
and then also an \htmladdnormallink{operator}{http://planetphysics.us/encyclopedia/QuantumSpinNetworkFunctor2.html} \emph{weak} topology to be defined on $B(\H)$.

\end{definition}

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