Hilbert C-bimodules and continuous Cuntz-Krieger algebras

• KAJIWARA Tsuyoshi

  Department of Environmental and Mathematical Sciences Okayama University

• WATATANI Yasuo

  Graduate School of Mathematics Kyushu University

書誌事項

タイトル別名

• Hilbert C<SUP>*</SUP>-bimodules and continuous Cuntz-Krieger algebras

抄録

We consider certain correspondences on disjoint unions Ω of circles which naturally give Hilbert C^*-bimodules X over circle algebras A. The bimodules X generate C^*-algebras \mathcal{O}_X 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 Pimsner's result.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 54 (1), 35-59, 2002

  一般社団法人 日本数学会

キーワード

• Hilbert $C^{*}$-bimodules
• $C^{*}$-algebras
• <i>K</i>-theory

詳細情報

• CRID: 1390282680091272320
• NII論文ID: 10007767471
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/1191593954
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 1864927
• NDL書誌ID: 6080250
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I6080250
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可