Fundamental groupoids of k-graphs
Combinatorics
2007-05-23 v1 Operator Algebras
Abstract
k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop a theory of the fundamental groupoid of a k-graph, and relate it to the fundamental groupoid of an associated graph called the 1-skeleton. We also explore the failure, in general, of k-graphs to faithfully embed into their fundamental groupoids.
Keywords
Cite
@article{arxiv.math/0401016,
title = {Fundamental groupoids of k-graphs},
author = {David Pask and John Quigg and Iain Raeburn},
journal= {arXiv preprint arXiv:math/0401016},
year = {2007}
}
Comments
12 pages