The $C^*$-algebras of finitely aligned higher-rank graphs

Details The $C^*$-algebras of finitely aligned higher-rank graphs The $C^*$-algebras of finitely aligned higher-rank graphs

2003-05-27

arxiv.org/abs/math/0305370v1

Mathematics

Operator Algebras

27 pages

Scientific paper

We generalise the theory of Cuntz-Krieger families and graph algebras to the class of finitely aligned $k$-graphs. This class contains in particular all row-finite $k$-graphs. The Cuntz-Krieger relations for non-row-finite $k$-graphs look significantly different from the usual ones, and this substantially complicates the analysis of the graph algebra. We prove a gauge-invariant uniqueness theorem and a Cuntz-Krieger uniqueness theorem for the $C^*$-algebras of finitely aligned $k$-graphs.

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