Hilbert C^*-bimodules and continuous Cuntz-Krieger algebras

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概要

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• We consider certain correspondences on disjoint unions Ω of circles which naturally give Hilbert C<SUP>*</SUP>-bimodules X over circle algebras A. The bimodules X generate C<SUP>*</SUP>-algebras \mathcal{O}<SUB>X</SUB> 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 (II)-freeness previously discussed by the authors. More precisely, we have a bijective correspondence between the set of closed two sided ideals of \mathcal{O}_{\bm{X}} and saturated hereditary open subsets of Ω. We also note that a formula of K-groups given by Deaconu is given without any minimality condition by just applying Pimsners result.

• 社団法人 日本数学会の論文

著者

• Watatani Yasuo

  Graduate School Of Mathematics Kyushu University

• Yasuo Watatani

  Graduate School Of Mathematics Kyushu University

• KAJIWARA Tsuyoshi

  Department of Environmental and Mathematical Sciences Okayama University

• Tsuyoshi Kajiwara

  Department Of Environmental And Mathematical Sciences Okayama University

• KAJIWARA Tsuyoshi

  Department of Applied Mathematics Faculty of Engineering Science Osaka University

関連論文

• GRAPHS AND KOLMOGOROV'S COMPLEXITY
• SPECTRA AND CHROMATIC NUMBERS OF INFINITE GRAPHS
• Hilbert C^*-bimodules and continuous Cuntz-Krieger algebras
• Induced Traces on Coaction Crosses Product $C^\ast$-algebras
• Group extensions and Plancherel formulas
• Traces on group extensions and C*-crossed products
• KMS STATES ON FINITE-GRAPH C∗-ALGEBRAS

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