Coverings of k-graphs
Operator Algebras
2008-05-23 v2 Combinatorics
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 the theory of covering spaces for k-graphs, obtaining a satisfactory version of the usual topological classification in terms of subgroups of a fundamental group. We then use this classification to describe the C*-algebras of covering k-graphs as crossed products by coactions of homogeneous spaces, generalizing recent results on the C*-algebras of graphs.
Keywords
Cite
@article{arxiv.math/0401017,
title = {Coverings of k-graphs},
author = {David Pask and John Quigg and Iain Raeburn},
journal= {arXiv preprint arXiv:math/0401017},
year = {2008}
}
Comments
Corrected a minor error in the proof of Theorem 7.1