Topological Quivers

By P. Muhly, M. Tomforde. 2003

59 citations recorded by the source corpus.

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 fromQ. 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.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3a9f7ee24f1a3818ffbff45d532286db35aa280d

Citations in the corpus

• Adding tails to $C^*$-correspondences (2002, unknown): “By adding tails to topological quivers in [17] the authors are able to reduce their analyses to the case when there are no sinks, or equivalently, to the case when the left action of the associated C∗-correspondence is injective.”