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• # Artykuł - szczegóły

## Studia Mathematica

2011 | 204 | 2 | 155-185

## The path space of a higher-rank graph

EN

### Abstrakty

EN
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.

155-185

wydano
2011

### Twórcy

autor
• School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia