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

Raeburn, Iain; Sims, Aidan; Yeend, Trent

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

Authors

Raeburn, Iain

Sims, Aidan

Yeend, Trent

Description

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.
27 pages