Obstructions to a general characterization of graph correspondences

Steven Kaliszewski; Nura Patani; John Quigg

doi:10.1017/S1446788713000177

Obstructions to a general characterization of graph correspondences

Steven Kaliszewski, Nura Patani, John Quigg

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English (US)
Pages (from-to)	169-188
Number of pages	20
Journal	Journal of the Australian Mathematical Society
Volume	95
Issue number	2
DOIs	https://doi.org/10.1017/S1446788713000177
State	Published - Oct 2013

Keywords

C*-correspondences
Hilbert modules
K-graphs
Topological graphs

ASJC Scopus subject areas

Mathematics(all)

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10.1017/S1446788713000177

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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.",

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author = "Steven Kaliszewski and Nura Patani and John Quigg",

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AU - Patani, Nura

AU - Quigg, John

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AB - 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.

KW - C-correspondences

KW - Hilbert modules

KW - K-graphs

KW - Topological graphs

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ER -

Obstructions to a general characterization of graph correspondences

Abstract

Keywords

ASJC Scopus subject areas

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