Skip to main content
SpringerLink
Log in

Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

In a previous work, the authors showed that the C*-algebra C*(Λ) of a row-finite higher-rank graph Λ with no sources is simple if and only if Λ is both cofinal and aperiodic. In this paper, we generalise this result to row-finite higher-rank graphs which are locally convex (but may contain sources). Our main tool is Farthing’s “removing sources” construction which embeds a row-finite locally convex higher-rank graph in a row-finite higher-rank graph with no sources in such a way that the associated C*-algebras are Morita equivalent.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Allen, D. Pask and A. Sims, A dual graph construction for higher-rank graphs, and K-theory for finite 2-graphs, Proceedings of the American Mathematical Society 134 (2006), 455–464.

    Article  MathSciNet  Google Scholar 

  2. T. Bates, D. Pask, I. Raeburn and W. Szymański, The C*-algebras of row-finite graphs, New York Journal of Mathematics 6 (2000), 307–324.

    MathSciNet  MATH  Google Scholar 

  3. J. Cuntz and W. Krieger, A class of C*-algebras and topological Markov chains, Inventiones Mathematicae 56 (1980), 251–268.

    Article  MathSciNet  Google Scholar 

  4. M. Enomoto and Y. Watatani, A graph theory for C*-algebras, Mathematica Japonica 25 (1980), 435–442.

    MathSciNet  MATH  Google Scholar 

  5. C. Farthing, Removing sources from higher-rank graphs, Journal of Operator Theory 60 (2008), 165–198.

    MathSciNet  MATH  Google Scholar 

  6. A. Kumjian and D. Pask, Higher-rank graph C*-algebras, New York Journal of Mathematics 6 (2000), 1–20.

    MathSciNet  MATH  Google Scholar 

  7. A. Kumjian, D. Pask and I. Raeburn, Cuntz-Krieger algebras of directed graphs, Pacific Journal of Mathematics 184 (1998), 161–174.

    Article  MathSciNet  Google Scholar 

  8. A. Kumjian, D. Pask, I. Raeburn and J. Renault, Graphs, groupoids and Cuntz-Krieger algebras, Journal of Functional Analysis 144 (1997), 505–541.

    Article  MathSciNet  Google Scholar 

  9. S. Mac Lane, Categories for the Working Mathematician, 2nd ed., Graduate Texts in Mathematics, Vol. 5. Springer-Verlag, New York, 1998.

    Google Scholar 

  10. I. Raeburn, Graph Algebras, CBMS Regional Conference Series in Mathematics, vol. 103, American Mathematical Society, 2005.

  11. I. Raeburn, A. Sims and T. Yeend, Higher-rank graphs and their C*-algebras, Proceedings of the Edinburgh Mathematical Society. Series II 46 (2003), 99–115.

    Article  MathSciNet  Google Scholar 

  12. I. Raeburn, A. Sims and T. Yeend, The C*-algebras of finitely aligned higher-rank graphs, Journal of Functional Analysis 213 (2004), 206–240.

    Article  MathSciNet  Google Scholar 

  13. I. Raeburn and D. P. Williams, Morita Equivalence and Continuous-Trace C*-Algebras, Mathematical Surveys and Monographs, vol. 60, 1998.

  14. D. I. Robertson and A. Sims, Simplicity of C*-algebras associated to higher-rank graphs, Proceedings of the London Mathematical Society 39 (2007), 337–344.

    MathSciNet  MATH  Google Scholar 

  15. G. Robertson and T. Steger, Affine buildings, tiling systems and higher-rank Cuntz-Krieger algebras, Journal für die reine und angewandte Mathematik 513 (1999), 115–144.

    Article  MathSciNet  Google Scholar 

  16. G. Robertson and T. Steger, Asymptotic K-theory for groups acting on Ã2 buildings, Canadian Journal of Mathematics 53 (2001), 809–833.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut for Matematik og Datalogi (IMADA), Syddansk Universitet, Campusvej 55, DK-5230, Odense M, Danmark

    David Robertson

  2. School of Mathematics and Applied Statistics, University of Wollongong, Austin Keane Building (15), NSW, 2522, Australia

    Aidan Sims

Authors
  1. David Robertson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aidan Sims
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Robertson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Robertson, D., Sims, A. Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs. Isr. J. Math. 172, 171–192 (2009). https://doi.org/10.1007/s11856-009-0070-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-009-0070-5

Keywords

Search

Navigation