The path space of a higher-rank graph

• Autorzy: Samuel B. G. Webster
• Języki publikacji: 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.

Kategorie tematyczne

• 46L05: General theory of C * -algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 204
• Numer: 2
• Strony: 155-185

Daty

wydano

2011

Twórcy

autor

Samuel B. G. Webster

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

Identyfikatory

DOI

10.4064/sm204-2-4