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.
- Cuntz-Krieger algebra
- graph algebra