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

Authors

Stephen Allen, University of NewcastleFollow
David Pask, University of NewcastleFollow
Aidan Sims, University of WollongongFollow

RIS ID

16512

Publication Details

Allen, S., Pask, D. A. & Sims, A. D. (2006). A dual graph construction for higher-rank graphs, and K-theory for finite 2-graphs. Proceedings of the American Mathematical Society, 134 (2), 455-464.

Abstract

Given a k-graph Λ and an element p of N^k, we define the dual k-graph, pΛ. We show that when Λ is row-finite and has no sources, the C*-algebras C*(Λ) and C*(pΛ) coincide. We use this isomorphism to apply Robertson and Steger's results to calculate the K-theory of C*(Λ) when Λ is finite and strongly connected and satisfies the aperiodicity condition.