Higher-rank graph algebras are iterated Cuntz-Pimsner algebras

This is the authors' abstract. We don't add key points for this paper.

Given a finitely aligned k-graph $Λ$, we let Λⁱ denote the $(k-1)$-graph formed by removing all edges of degree eᵢ from $Λ$. We show that the Toeplitz-Cuntz-Krieger algebra of $Λ$, denoted by TC^*(Λ), may be realised as the Toeplitz algebra of a Hilbert TC^*(Λⁱ)-bimodule. When $Λ$ is locally-convex, we show that the Cuntz-Krieger algebra of $Λ$, which we denote by C^*(Λ), may be realised as the Cuntz-Pimsner algebra of a Hilbert C^*(Λⁱ)-bimodule. Consequently, TC^*(Λ) and C^*(Λ) may be viewed as iterated Toeplitz and iterated Cuntz-Pimsner algebras over c₀(Λ⁰) respectively.