Coverings of k-graphs

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.

Corrected a minor error in the proof of Theorem 7.1

References in corpus (2)

• Skew products and crossed products by coactions
• Some intrinsic properties of simple graph $C^{\ast }$-algebras

Cited by in corpus (1)

• Fundamental groupoids of k-graphs