PlanetMath: representation of a $C_c(\mathsf{G}) $ *- topological algebra

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representation of a $C_c(\mathsf{G})$ *- topological algebra

(Definition)

Definition 0.1 A representation of a $C_c({\mathsf{G}})$ topological

-algebra is defined as
a continuous

-morphism from $C_c({\mathsf{G}})$ to $B(\H )$ , where ${\mathsf{G}}$ is a topological groupoid, (usually a locally compact groupoid, ${\mathsf{G}}_{lc}$ ), $\H$ is a Hilbert space, and $B(\H )$ is the

-algebra of bounded linear operators on the Hilbert space $\H$ ; of course, one considers the inductive limit (strong) topology to be defined on $C_c({\mathsf{G}})$ , and then also an operator weak topology to be defined on $B(\H )$ .

"representation of a $C_c(\mathsf{G})$ *- topological algebra" is owned by bci1.

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See Also:

Other names:

groupoid C*-algebra representations

Also defines:

representation of a topological *- algebra

Keywords:

representation of *-algebra on $B(\H)$ , the $C^*$

-algebra of bounded operators on the Hilbert space $\H$

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AMS MSC:	55U40 (Algebraic topology :: Applied homological algebra and category theory :: Topological categories, foundations of homotopy theory)
	55P10 (Algebraic topology :: Homotopy theory :: Homotopy equivalences)
	55N20 (Algebraic topology :: Homology and cohomology theories :: Generalized homology and cohomology theories)
	55N33 (Algebraic topology :: Homology and cohomology theories :: Intersection homology and cohomology)
	18D05 (Category theory; homological algebra :: Categories with structure :: Double categories, $2$-categories, bicategories and generalizations)
	81-00 (Quantum theory :: General reference works )

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