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.
Original language | English (US) |
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Pages (from-to) | 161-191 |
Number of pages | 31 |
Journal | Journal of Algebra |
Volume | 289 |
Issue number | 1 |
DOIs | |
State | Published - Jul 1 2005 |
Keywords
- C*-algebra
- Coaction
- Covering
- Fundamental group
- Small category
- k-Graph
ASJC Scopus subject areas
- Algebra and Number Theory