Hilbert C*-bimodules and countably generated Cuntz-Krieger algebras

T. Kajiwara, C. Pinzari, Yasuo Watatani

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Results by Cuntz and Kreiger on uniqueness, simplicity and the ideal structure of the algebras OA associated with finite matrices with entries in {0, 1} are generalized to the case where A is an infinite matrix whose rows and columns are eventually zero, but not identically zero. Similar results have been recently obtained by Kumjian, Pask, Raeburn and Renault from the viewpoint of Renault's theory of groupoids. An alternative approach, based on the realization of OA as an algebra generated by a Hilbert C*-bimodule introduced by Pimsner, is proposed and compared.

Original languageEnglish
Pages (from-to)3-18
Number of pages16
JournalJournal of Operator Theory
Volume45
Issue number1
Publication statusPublished - 2001

Fingerprint

Cuntz-Krieger Algebra
Bimodule
Hilbert
Algebra
Infinite Matrices
Groupoids
Zero
Simplicity
Uniqueness
Alternatives

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Kajiwara, T., Pinzari, C., & Watatani, Y. (2001). Hilbert C*-bimodules and countably generated Cuntz-Krieger algebras. Journal of Operator Theory, 45(1), 3-18.

Hilbert C*-bimodules and countably generated Cuntz-Krieger algebras. / Kajiwara, T.; Pinzari, C.; Watatani, Yasuo.

In: Journal of Operator Theory, Vol. 45, No. 1, 2001, p. 3-18.

Research output: Contribution to journalArticle

Kajiwara, T, Pinzari, C & Watatani, Y 2001, 'Hilbert C*-bimodules and countably generated Cuntz-Krieger algebras', Journal of Operator Theory, vol. 45, no. 1, pp. 3-18.
Kajiwara, T. ; Pinzari, C. ; Watatani, Yasuo. / Hilbert C*-bimodules and countably generated Cuntz-Krieger algebras. In: Journal of Operator Theory. 2001 ; Vol. 45, No. 1. pp. 3-18.
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