Coverings of k-graphs

Details Coverings of k-graphs Coverings of k-graphs

2004-01-03

arxiv.org/abs/math/0401017v2

J. Algebra 289 (2005), 161-191

Mathematics

Operator Algebras

Corrected a minor error in the proof of Theorem 7.1

Scientific paper

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.

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