C*-algebras associated to coverings of k-graphs

Authors

Alexander Kumjian, University of Nevada - Reno
David A. Pask, University of WollongongFollow
Aidan Sims, University of Wollongong

RIS ID

24138

Publication Details

Kumjian, A., Pask, D. A. & Sims, A. D. (2008). C*-algebras associated to coverings of k-graphs. Documenta Mathematica, Band 13 161-205.

Abstract

A covering of k-graphs (in the sense of Pask-Quigg- Raeburn) induces an embedding of universal C∗-algebras. We show how to build a (k + 1)-graph whose universal algebra encodes this embedding. More generally we show how to realise a direct limit of k-graph algebras under embeddings induced from coverings as the universal algebra of a (k +1)-graph. Our main focus is on computing the K-theory of the (k+1)-graph algebra from that of the component k-graph algebras.

Examples of our construction include a realisation of the Kirchberg algebra Pn whose K-theory is opposite to that of On, and a class of AT-algebras that can naturally be regarded as higher-rank Bunce- Deddens algebras.

Link to publisher version (URL)

Documenta Mathematica