Skip to main content
placeholder image

C*-algebras associated to coverings of k-graphs

Journal Article


Download full-text (Open Access)

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 P_n whose K-theory is opposite to that of O_n, and a class of

    AT-algebras that can naturally be regarded as higher-rank Bunce-

    Deddens algebras.

Publication Date


  • 2008

Citation


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

Scopus Eid


  • 2-s2.0-58149252145

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=10463&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3127

Number Of Pages


  • 44

Start Page


  • 161

End Page


  • 205

Volume


  • Band 13

Place Of Publication


  • http://www.mathematik.uni-bielefeld.de/documenta/

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 P_n whose K-theory is opposite to that of O_n, and a class of

    AT-algebras that can naturally be regarded as higher-rank Bunce-

    Deddens algebras.

Publication Date


  • 2008

Citation


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

Scopus Eid


  • 2-s2.0-58149252145

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=10463&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3127

Number Of Pages


  • 44

Start Page


  • 161

End Page


  • 205

Volume


  • Band 13

Place Of Publication


  • http://www.mathematik.uni-bielefeld.de/documenta/