Coverings of k-graphs

David Pask, John Quigg, Iain Raeburn

Research output: Contribution to journalArticle

22 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)161-191
Number of pages31
JournalJournal of Algebra
Volume289
Issue number1
DOIs
StatePublished - Jul 1 2005

Fingerprint

Covering
Graph in graph theory
C*-algebra
Coaction
Covering Space
Operator Algebras
Crossed Product
Homogeneous Space
Fundamental Group
Directed Graph
Subgroup
Analogue
Model

Keywords

  • C*-algebra
  • Coaction
  • Covering
  • Fundamental group
  • k-Graph
  • Small category

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Coverings of k-graphs. / Pask, David; Quigg, John; Raeburn, Iain.

In: Journal of Algebra, Vol. 289, No. 1, 01.07.2005, p. 161-191.

Research output: Contribution to journalArticle

Pask, David ; Quigg, John ; Raeburn, Iain. / Coverings of k-graphs. In: Journal of Algebra. 2005 ; Vol. 289, No. 1. pp. 161-191.
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