The path space of a higher-rank graph

Samuel B. G. Webster. "The path space of a higher-rank graph." Studia Mathematica 204.2 (2011): 155-185. <http://eudml.org/doc/285764>.

@article{SamuelB2011,
abstract = {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.},
author = {Samuel B. G. Webster},
journal = {Studia Mathematica},
keywords = {graph algebra; -graph; higher-rank graph},
language = {eng},
number = {2},
pages = {155-185},
title = {The path space of a higher-rank graph},
url = {http://eudml.org/doc/285764},
volume = {204},
year = {2011},
}

TY - JOUR
AU - Samuel B. G. Webster
TI - The path space of a higher-rank graph
JO - Studia Mathematica
PY - 2011
VL - 204
IS - 2
SP - 155
EP - 185
AB - 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.
LA - eng
KW - graph algebra; -graph; higher-rank graph
UR - http://eudml.org/doc/285764
ER -