Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T03:07:16.308Z Has data issue: false hasContentIssue false
  • English
  • Français

THE C*-ALGEBRAS OF LATTICE ATOMIC GRAPHS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  29 June 2009

YANGPING JING
YANGPING JING*
Affiliation:
The School of Science, Hangzhou Dianzi University, Hangzhou 310018, PR China (email: [email protected])
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.

In this article, we define lattice graphs (which generalise ultragraphs) as well as their Cuntz–Krieger families and C*-algebras. We will give a thorough study in the special case of lattice atomic graphs.

Keywords

lattice atomic graphCuntz–Krieger familylattice graph C*-algebra

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 3 , December 2009 , pp. 393 - 401
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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]Blackadar, B., ‘Shape theory for C *-algebras’, Math. Scand. 56 (1985), 249–275.CrossRefGoogle Scholar
[3]Blyth, T. S., Lattices and Ordered Algebraic Structures (Springer, Berlin, 2005).Google Scholar
[4]Coburn, L. A., ‘The C *-algebra generated by an isometry II’, Trans. Amer. Math. Soc. 137 (1969), 211–217.Google Scholar
[5]Drinen, D. and Tomforde, M., ‘The C *-algebras of arbitrary graphs’, Rocky Mountain J. Math. 35 (2005), 105–135.CrossRefGoogle Scholar
[6]Exel, R. and Laca, M., ‘Cuntz–Krieger algebras for infinite matrices’, J. Reine Angew. Math. 512 (1999), 119–172.CrossRefGoogle Scholar
[7]an Huef, A. and Raeburn, I., ‘The ideal structure of Cuntz–Krieger algebras’, Ergod. Th. & Dynam. Sys. 17 (1997), 611–624.Google Scholar
[8]Katsura, T., Muhly, P. S., Sims, A. and Tomforde, M., ‘Ultragraph C *-algeras via topological quivers’, Studia Math. 187 (2008), 137–155.CrossRefGoogle Scholar
[9]Kumjian, A., Pask, D. and Raeburn, I., ‘Cuntz–Krieger algebras of directed graphs’, Pacific J. Math. 184 (1998), 161–174.CrossRefGoogle Scholar
[10]Kumjian, A., Pask, D., Raeburn, I. and Renault, J., ‘Graphs, groupoids, and Cuntz–Krieger algebras’, J. Funct. Anal. 144 (1997), 505–541.CrossRefGoogle Scholar
[11]Tomforde, M., ‘A unified approach to Exel-Laca algebras an C *-algebras associated to graphs’, J. Operator Theory 50 (2003), 345–368.Google Scholar
[12]Tomforde, M., ‘Simplicity of ultragraph algebras’, Indiana Univ. Math. J. 52 (2003), 901–926.CrossRefGoogle Scholar