Twisted k-graph algebras associated to Bratteli diagrams

2015 Springer Basel Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite traces of the resulting twisted (k + 1)-graph C*-algebras. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are matrix algebras over noncommutative tori. For such systems we calculate the ordered K-theory of the resulting twisted 3-graph C*-algebras. We deduce that every such C*-algebra is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the sense of Pask-Raeburn-Rørdam-Sims.