Hilbert C*-bimodules and continuous Cuntz-Krieger algebras

Tsuyoshi Kajiwara, Yasuo Watatani

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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 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 (II)-freeness previously discussed by the authors. More precisely, we have a bijective correspondence between the set of closed two sided ideals of OX 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.

Original languageEnglish
Pages (from-to)35-59
Number of pages25
JournalJournal of the Mathematical Society of Japan
Volume54
Issue number1
Publication statusPublished - 2002

Fingerprint

Cuntz-Krieger Algebra
Bimodule
Hilbert
Circle
Correspondence
Algebra
K-group
Groupoid
Minimality
Bijective
C*-algebra
Simplicity
Disjoint
Union
Isomorphic
Closed
Subset

Keywords

  • C-algebras
  • Hilbert C-bimodules
  • K-theory

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Hilbert C*-bimodules and continuous Cuntz-Krieger algebras. / Kajiwara, Tsuyoshi; Watatani, Yasuo.

In: Journal of the Mathematical Society of Japan, Vol. 54, No. 1, 2002, p. 35-59.

Research output: Contribution to journalArticle

@article{e99f77914b2f410496bc3e6673681471,
title = "Hilbert C*-bimodules and continuous Cuntz-Krieger algebras",
abstract = "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 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 (II)-freeness previously discussed by the authors. More precisely, we have a bijective correspondence between the set of closed two sided ideals of OX 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.",
keywords = "C-algebras, Hilbert C-bimodules, K-theory",
author = "Tsuyoshi Kajiwara and Yasuo Watatani",
year = "2002",
language = "English",
volume = "54",
pages = "35--59",
journal = "Journal of the Mathematical Society of Japan",
issn = "0025-5645",
publisher = "Mathematical Society of Japan - Kobe University",
number = "1",

}

TY - JOUR

T1 - Hilbert C*-bimodules and continuous Cuntz-Krieger algebras

AU - Kajiwara, Tsuyoshi

AU - Watatani, Yasuo

PY - 2002

Y1 - 2002

N2 - 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 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 (II)-freeness previously discussed by the authors. More precisely, we have a bijective correspondence between the set of closed two sided ideals of OX 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.

AB - 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 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 (II)-freeness previously discussed by the authors. More precisely, we have a bijective correspondence between the set of closed two sided ideals of OX 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.

KW - C-algebras

KW - Hilbert C-bimodules

KW - K-theory

UR - http://www.scopus.com/inward/record.url?scp=0036069247&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036069247&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036069247

VL - 54

SP - 35

EP - 59

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 1

ER -