Topological Quivers
| dc.creator | Muhly, Paul S. | |
| dc.creator | Tomforde, Mark | |
| dc.date | 2003-12-04 | |
| dc.date | 2005-03-01 | |
| dc.date.accessioned | 2026-07-07T05:03:34Z | |
| dc.date.available | 2026-07-07T05:03:34Z | |
| dc.description | 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. | |
| dc.description | 55 pages, uses XY-pic. A few typos corrected. This is the version that will be published | |
| dc.identifier | https://arxiv.org/abs/math/0312109 | |
| dc.identifier | http://arxiv.org/abs/math/0312109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69471 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L55; 46L08 | |
| dc.title | Topological Quivers | |
| dc.type | text |