Browsing by Author "McCann, Shawn Josephs"
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- ItemOpen AccessC*-algebras associated with topological group quivers(2012) McCann, Shawn Josephs; Brenken, BerndtTopological 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 r a locally compact group and a and (3 endomorphisms on r, one may construct a topological quiver Qae,,a(r) with vertex set r, and edge set n ,,8 (r) = { ( X ) y) E r X r I a(y) = (3( X)}. In this dissertation, the author examines the Cuntz-Pimsner algebra C* ( Q a,,B (r)). The investigative topics include generators of the C*-algebras, spatial structure (i.e., colimits, tensor products and crossed products), K-groups, simplicity, and lattice properties.