The path space of a higher-rank graph

@article{Webster2011ThePS,
  title={The path space of a higher-rank graph},
  author={Samuel G. Webster},
  journal={Studia Mathematica},
  year={2011},
  volume={204},
  pages={155-185}
}
  • Samuel G. Webster
  • Published 2011
  • Mathematics
  • Studia Mathematica
  • We construct a locally compact Hausdorff topology on the path space of a finitely aligned $k$-graph $\Lambda$. We identify the boundary-path space $\partial\Lambda$ as the spectrum of a commutative $C^*$-subalgebra $D_\Lambda$ of $C^*(\Lambda)$. Then, using a construction similar to that of Farthing, we construct a finitely aligned $k$-graph $\wt\Lambda$ with no sources in which $\Lambda$ is embedded, and show that $\partial\Lambda$ is homeomorphic to a subset of $\partial\wt\Lambda$ . We show… CONTINUE READING

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