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

Abstract

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 $C^{\ast }(p\Lambda )$ coincide. We use this isomorphism to apply Robertson and Steger's results to calculate the $K$-theory of $C^{\ast }(\Lambda )$ when $\Lambda$ is finite and strongly connected and satisfies the aperiodicity condition.

9 pages

Cited by in corpus (1)

• The $H^{\infty }$ algebras of higher rank graphs