Skip to main content Accessibility help
×
Home

C *-Algebras of Infinite Graphs and Cuntz-Krieger Algebras

  • Berndt Brenken (a1)

Abstract

The Cuntz-Krieger algebra ${{\mathcal{O}}_{B}}$ is defined for an arbitrary, possibly infinite and infinite valued, matrix $B$ . A graph ${{C}^{*}}$ -algebra ${{G}^{*}}\left( E \right)$ is introduced for an arbitrary directed graph $E$ , and is shown to coincide with a previously defined graph algebra ${{C}^{*}}\left( E \right)$ if each source of $E$ emits only finitely many edges. Each graph algebra ${{G}^{*}}\left( E \right)$ is isomorphic to the Cuntz-Krieger algebra ${{\mathcal{O}}_{B}}$ where $B$ is the vertex matrix of $E$ .

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      C *-Algebras of Infinite Graphs and Cuntz-Krieger Algebras
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      C *-Algebras of Infinite Graphs and Cuntz-Krieger Algebras
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      C *-Algebras of Infinite Graphs and Cuntz-Krieger Algebras
      Available formats
      ×

Copyright

References

Hide All
[1] an Huef, A. and Raeburn, I., The ideal structure of Cuntz-Krieger algebras. Ergodic Theory Dynamical Systems 17 (1997), 171997.
[2] Brenken, B., Cuntz-Krieger algebras and endomorphisms of finite direct sums of type I factors. Trans. Amer.Math. Soc., to appear.
[3] Cuntz, J. and Krieger, W., A class of C*-algebras and topological Markov chains. Invent.Math. 56 (1980), 561980.
[4] Exel, R. and Laca, M., Cuntz-Krieger algebras for infinite matrices. J. Reine Angew. Math, to appear.
[5] Fowler, N., Laca, M., and Raeburn, I., The C*-algebras of infinite graphs. Preprint, 1998.
[6] Kumjian, A., Pask, D. and Raeburn, I., Cuntz-Krieger algebras of directed graphs. Pacific J. Math. (1) 184 (1998), 1841998.
[7] Kumjian, A., Pask, D., Raeburn, I., and Renault, J., Graphs, Groupoids, and Cuntz-Krieger algebras. J. Funct. Anal. 144 (1997), 1441997.
[8] Lind, D. and Marcus, B., An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, 1995.
[9] Rordam, M., Classification of Cuntz-Krieger Algebras. K-theory 9 (1995), 91995.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Related content

Powered by UNSILO

C *-Algebras of Infinite Graphs and Cuntz-Krieger Algebras

  • Berndt Brenken (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.