Realising the Toeplitz algebra of a higher-rank graph as a Cuntz-Krieger algebra

Abstract

For a row-finite higher-rank graph Λ, we construct a higher-rank graph TΛ such that the Toeplitz algebra of Λ is isomorphic to the Cuntz-Krieger algebra of TΛ. We then prove that the higher-rank graph TΛ is always aperiodic and use this fact to give another proof of a uniqueness theorem for the Toeplitz algebras of higher-rank graphs.

References in corpus (6)

• Higher rank graph C*-algebras
• Simplicity of C*-algebras associated to higher-rank graphs
• Product systems of graphs and the Toeplitz algebras of higher-rank graphs
• Adding tails to C*-correspondences
• Simplicity of finitely-aligned k-graph C*-algebras
• The co-universal C*-algebra of a row-finite graph