Topological higher-rank graphs and the $C^*$-algebras of topological 1-graphs

Details Topological higher-rank graphs and the $C^*$-algebras of topological 1-graphs Topological higher-rank graphs and the $C^*$-algebras of topological 1-graphs

2005-09-20

arxiv.org/abs/math/0509445v2

Mathematics

Operator Algebras

13 pages

Scientific paper

We introduce the notion of a topological higher-rank graph, a unified
generalization of the higher-rank graph and the topological graph. Using
groupoid techniques, we define the Toeplitz and Cuntz-Krieger algebras of
topological higher-rank graphs, and show that the $C^*$-algebras defined are
coherent with the existing theory.

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