Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T16:04:46.249Z Has data issue: false hasContentIssue false
  • English
  • Français

Gauge-Invariant Ideals in the C*-Algebras of Finitely Aligned Higher-Rank Graphs

Published online by Cambridge University Press:  20 November 2018

Aidan Sims
Aidan Sims*
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia e-mail: Aidan.Sims@newcastle.edu.au
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We produce a complete description of the lattice of gauge-invariant ideals in ${{C}^{*}}(\Lambda )$ for a finitely aligned $k$-graph $\Lambda $. We provide a condition on $\Lambda $ under which every ideal is gauge-invariant. We give conditions on $\Lambda $ under which ${{C}^{*}}(\Lambda )$ satisfies the hypotheses of the Kirchberg–Phillips classification theorem.

Keywords

46L05Graphs as categoriesgraph algebraC*-algebra
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 6 , 01 December 2006 , pp. 1268 - 1290
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Bates, T., Pask, D., Raeburn, I., and Szymański, W., The C*-algebras of row–finite graphs. New York J. Math. 6(2000), 307–324.Google Scholar
[2] Bates, T., Hong, J., Raeburn, I., and Szymański, W., The ideal structure of the C*-algebras of infinite graphs. Illinois J. Math. 46(2002), no. 4, 1159–1176.Google Scholar
[3] Hong, J. H. and Szymański, W., The primitive ideal space of the C*-algebras of infinite graphs. J. Math. Soc. Japan 56(2004), no. 1, 45–64.Google Scholar
[4] Kumjian, A. and Pask, D., Higher rank graph C*-algebras. New York J. Math. 6(2000), 1–2.Google Scholar
[5] Pask, D., Quigg, J. C., and Raeburn, I., Coverings of k-graphs. J. Algebra 289(2005), no. 1, 161–191.Google Scholar
[6] Phillips, N. C., A classification theorem for nuclear purely infinite simple C*-algebras. Documenta Math. 5(2000), 49–114.Google Scholar
[7] Quigg, J. C., Discrete C*-coactions and C*-algebraic bundles. J. Austral. Math. Soc. Ser. A 60(1996), no. 2, 204–221.Google Scholar
[8] Raeburn, I. and Sims, A., Product systems of graphs and the Toeplitz algebras of higher-rank graphs. J. Operator Theory 53(2005), 399–429.Google Scholar
[9] Raeburn, I., Sims, A. and Yeend, T., Higher-rank graphs and their C*-algebras.. Proc. Edinb. Math. Soc. 46(2003), 99–115.Google Scholar
[10] Raeburn, I., Sims, A. and Yeend, T., The C*-algebras of finitely aligned higher-rank graphs. J. Funct. Anal. 213(2004), no. 1, 206–240.Google Scholar
[11] Rosenberg, J. and Schochet, C., The Künneth theorem and the universal coefficient theorem for Kasparov's generalised K-functor. Duke Math. J. 55(1987), no. 2, 431–474.Google Scholar
[12] Sims, A., Relative Cuntz–Krieger algebras of finitely aligned higher-rank graphs. Indiana Univ. Math. J. 55(2006), 849–869.Google Scholar
[13] Szymański, W., Simplicity of Cuntz-Krieger algebras of infinite matrices, Pacific J. Math. 199(2001), no. 1, 249–256.Google Scholar