A dual graph construction for higher-rank graphs, and $K$-theory for finite 2-graphs

Stephen Allen, David Pask, Aidan Sims

Given a $k$-graph $\Lambda$ and an element $p$ of $\NN^k$, we define the dual $k$-graph, $p\Lambda$. We show that when $\Lambda$ is row-finite and has no sources, the $C^{\ast }$-algebras $C^{\ast }(\Lambda )$ and $C^…