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- W59292788 abstract "Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a Cuntz-Pimsner algebra $C^*(Q).$ Given $Gamma$ a locally compact group and $alpha$ and $beta$ endomorphisms on $Gamma,$ one may construct a topological quiver $Q_{alpha,beta}(Gamma)$ with vertex set $Gamma,$ and edge set $Omega_{alpha,beta}(Gamma)= {(x,y)inGammatimesGammast alpha(y)=beta(x)}.$ In cite{Mc1}, the author examined the Cuntz-Pimsner algebra $cO_{alpha,beta}(Gamma):=C^*(Q_{alpha,beta}(Gamma))$ and found generators (and their relations) of $cO_{alpha,beta}(Gamma).$ In this paper, the author translates a known criterion for simplicity of topological quivers into a precise criterion for the simplicity of topological group relations." @default.
- W59292788 created "2016-06-24" @default.
- W59292788 creator A5073779621 @default.
- W59292788 date "2013-09-18" @default.
- W59292788 modified "2023-09-27" @default.
- W59292788 title "$C^*$-algebras associated with topological group quivers III: Simplicity Criterion" @default.
- W59292788 hasPublicationYear "2013" @default.
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