Obstructions to a general characterization of graph correspondences

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

For a countable discrete space V, every nondegenerate separable C*-correspondence over c0(V) is isomorphic to one coming from a directed graph with vertex set V. In this paper we demonstrate why the analogous characterizations fail to hold for higher-rank graphs (where one considers product systems of C*-correspondences) and for topological graphs (where V is locally compact Hausdorff), and we discuss the obstructions that arise.

Original languageEnglish (US)
Pages (from-to)169-188
Number of pages20
JournalJournal of the Australian Mathematical Society
Volume95
Issue number2
DOIs
StatePublished - Oct 2013

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Obstruction
Correspondence
Topological Graph
Product Systems
Locally Compact
Graph in graph theory
Directed Graph
Countable
Isomorphic
Vertex of a graph
Demonstrate

Keywords

  • C*-correspondences
  • Hilbert modules
  • K-graphs
  • Topological graphs

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Obstructions to a general characterization of graph correspondences. / Kaliszewski, Steven; Patani, Nura; Quigg, John.

In: Journal of the Australian Mathematical Society, Vol. 95, No. 2, 10.2013, p. 169-188.

Research output: Contribution to journalArticle

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