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OBSTRUCTIONS TO A GENERAL CHARACTERIZATION OF GRAPH CORRESPONDENCES
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 95 / Issue 2 / October 2013
- Published online by Cambridge University Press:
- 07 June 2013, pp. 169-188
- Print publication:
- October 2013
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- Article
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For a countable discrete space
$V$, every nondegenerate separable 
${C}^{\ast } $-correspondence over 
${c}_{0} (V)$ 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}^{\ast } $-correspondences) and for topological graphs (where 
$V$ is locally compact Hausdorff), and we discuss the obstructions that arise.
