2003/12/04 by Paul S. Muhly, Muhly, Paul S., Mark Tomforde +1 · 2 citations
Mathematics · #46L08 #46L55 #FOS: Mathematics #Operator Algebras (math.OA) #Rings, Modules, and Algebras #math.OA #msc:46L08 #msc:46L55
paper · pdf · doi:10.48550/arxiv.math/0312109
55 pages, uses XY-pic. A few typos corrected. This is the version that will be published
openalex publication_date 2003/12/04 · arxiv created 2005/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Topological quivers are generalizations of directed graphs in which the sets of vertices and edges are locally compact Hausdorff spaces. Associated to such a topological quiver Q is a C*-correspondence, and from this correspondence one may construct a Cuntz-Pimsner algebra C*(Q). In this paper we develop the general theory of topological quiver C*-algebras and show how certain C*-algebras found in the literature may be viewed from this general perspective. In particular, we show that C*-algebras of topological quivers generalize the well-studied class of graph C*-algebras and in analogy with that theory much of the operator algebra structure of C*(Q) can be determined from Q. We also show that many fundamental results from the theory of graph C*-algebras have natural analogues in the context of topological quivers (often with more involved proofs). These include the Gauge-Invariant Uniqueness theorem, the Cuntz-Krieger Uniqueness theorem, descriptions of the ideal structure, and conditions for simplicity.