The C∗-algebras of finitely aligned higher-rank graphs

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.