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A Dual Graph Construction For Higher-Rank Graphs, And K-Theory For Finite 2-Graphs, Stephen Allen, David Pask, Aidan Sims
A Dual Graph Construction For Higher-Rank Graphs, And K-Theory For Finite 2-Graphs, Stephen Allen, David Pask, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
Given a k-graph Λ and an element p of Nk, 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.