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

摘要

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