Hilbert C-bimodules and continuous Cuntz-Krieger algebras

We consider certain correspondences on disjoint unions \Omega of circles which naturally give Hilbert C^* -bimodules X over circle algebras A . The bimodules X generate C^* -algebras Ox which are isomorphic to a continuous version of Cuntz-Krieger algebras introduced by Deaconu using groupoid method...

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Bibliographic Details
Published in:Journal of the Mathematical Society of Japan 2002-01, Vol.54 (1), p.35-59
Main Authors: KAJIWARA, Tsuyoshi, WATATANI, Yasuo
Format: Article
Language:English
Subjects:
46L05
46L08
46L55
46L80
C^- algebras
Hilbert C^- bimodules
K-theory
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Summary:We consider certain correspondences on disjoint unions \Omega of circles which naturally give Hilbert C^* -bimodules X over circle algebras A . The bimodules X generate C^* -algebras Ox which are isomorphic to a continuous version of Cuntz-Krieger algebras introduced by Deaconu using groupoid method. We study the simplicity and the ideal structure of the algebras under some conditions using (I)-freeness and (\mathrm{II})- freeness previously discussed by the authors. More precisely, we have a bijective correspondence between the set of closed two sided ideals of \mathscr{O}_{X} and saturated hereditary open subsets of \Omega . We also note that a formula of K -groups given by Deaconu is given without any minimality condition by just applying Pimsner's result.
ISSN:0025-5645
1881-2333
DOI:10.2969/jmsj/1191593954