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The path space of a higher-rank graph

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Webster S.

Studia Mathematica

2011

tom 204

nr 2

155-185

We construct a locally compact Hausdorff topology on the path space of a finitely aligned k-graph Λ. We identify the boundary-path space ∂Λ as the spectrum of a commutative C*-subalgebra $D_{Λ}$ of C*(Λ). Then, using a construction similar to that of Farthing, we construct a finitely aligned k-graph Λ̃ with no sources in which Λ is embedded, and show that ∂Λ is homeomorphic to a subset of ∂Λ̃. We show that when Λ is row-finite, we can identify C*(Λ) with a full corner of C*(Λ̃), and deduce that $D_{Λ}$ is isomorphic to a corner of $D_{Λ̃}$. Lastly, we show that this isomorphism implements the homeomorphism between the boundary-path spaces.

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1 Studia Mathematica

1 Webster S.

1 2011

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The path space of a higher-rank graph