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- Title
TOPOLOGICAL QUIVERS.
- Authors
MUHLY, PAUL S.; TOMFORDE, MARK
- Abstract
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 $\mathcal{Q}$ is a C*-correspondence, and from this correspondence one may construct a Cuntz–Pimsner algebra $C^*(\mathcal{Q})$. 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 $C^*(\mathcal{Q})$ can be determined from $\mathcal{Q}$. 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.
- Subjects
TOPOLOGY; ALGEBRAIC topology; GEOMETRY; GRAPH theory; MATHEMATICS
- Publication
International Journal of Mathematics, 2005, Vol 16, Issue 7, p693
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X05003077