Gauge-invariant uniqueness theorem for P-graphs

Huben proved a gauge-invariant uniqueness theorem for P-graphs, by reducing to an amenable group and the theory of normal coactions. Here we employ instead the more recent theory of maximal coactions, and give an alternative version of the gauge-invariant uniqueness theorem. We also note that the coaction involved in Huben's original theorem is in fact the normalization of the (assumed given) maximal coaction. Our main emphasis is that the use of maximal coactions allows for a more direct and elementary approach, and moreover this method will be widely applicable. This is joint work with Robert Huben, S. Kaliszewski, and Nadia Larsen.