We generalise the theory of Cuntz–Krieger families andgraph 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 anda Cuntz–Krieger uniqueness theorem for the C*-algebras of finitely aligned k-graphs.
Journal of Functional Analysis Vol. 213, Issue 1, p. 206-240