We consider certain correspondences on disjoint unions of circles which naturally give Hilbert -bimodules over circle algebras . The bimodules generate -algebras 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 freeness previously discussed by the authors. More precisely, we have a bijective correspondence between the set of closed two sided ideals of and saturated hereditary open subsets of . We also note that a formula of -groups given by Deaconu is given without any minimality condition by just applying Pimsner's result.
"Hilbert -bimodules and continuous Cuntz-Krieger algebras." J. Math. Soc. Japan 54 (1) 35 - 59, January, 2002. https://doi.org/10.2969/jmsj/1191593954