PlanetPhysics/Representation of a CcG Topological Algebra

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A \htmladdnormallink{representation {http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html} of a [[../C_cG/|Failed to parse (unknown function "\grp"): {\displaystyle C_c(\grp)}
]] [[../CoIntersections/|topological]] $*$--algebra} is defined as a continuous $*$--morphism from Failed to parse (unknown function "\grp"): {\displaystyle C_c(\grp)}
 to $B(ℍ)$, where Failed to parse (unknown function "\grp"): {\displaystyle \grp}
 is a \htmladdnormallink{topological groupoid {http://planetphysics.us/encyclopedia/GroupoidHomomorphism2.html}, (usually a [[../LocallyCompactGroupoid/|locally compact groupoid]], Failed to parse (unknown function "\grp"): {\displaystyle \grp_{lc}}
), $ℍ$ is a \htmladdnormallink{Hilbert space}}{http://planetphysics.us/encyclopedia/NormInducedByInnerProduct.html}, and $B(ℍ)$ is the $C^{*}$-algebra of bounded [[../Commutator/|linear operators]] on the Hilbert space $ℍ$; of course, one considers the inductive limit (strong) topology to be defined on Failed to parse (unknown function "\grp"): {\displaystyle C_c(\grp)}
,

and then also an [[../QuantumSpinNetworkFunctor2/|operator]] weak topology to be defined on $B(ℍ)$.