### Abstract

This is the final one in the series of papers where we introduce and study the C^{*}-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated C^{*}-algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as C^{*}-algebras associated with topological graphs.

Original language | English |
---|---|

Pages (from-to) | 1161-1187 |

Number of pages | 27 |

Journal | Journal of Functional Analysis |

Volume | 254 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2008 Mar 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- C-algebra
- Dynamical system
- Graph algebra
- Homeomorphism C-algebra
- K-theory
- Kirchberg algebra
- Purely infinite
- Topological graph

### ASJC Scopus subject areas

- Analysis

### Cite this

**A class of C ^{*}-algebras generalizing both graph algebras and homeomorphism C^{*}-algebras IV, pure infiniteness.** / Katsura, Takeshi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A class of C*-algebras generalizing both graph algebras and homeomorphism C*-algebras IV, pure infiniteness

AU - Katsura, Takeshi

PY - 2008/3/1

Y1 - 2008/3/1

N2 - This is the final one in the series of papers where we introduce and study the C*-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated C*-algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as C*-algebras associated with topological graphs.

AB - This is the final one in the series of papers where we introduce and study the C*-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated C*-algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as C*-algebras associated with topological graphs.

KW - C-algebra

KW - Dynamical system

KW - Graph algebra

KW - Homeomorphism C-algebra

KW - K-theory

KW - Kirchberg algebra

KW - Purely infinite

KW - Topological graph

UR - http://www.scopus.com/inward/record.url?scp=38649143653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38649143653&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2007.11.014

DO - 10.1016/j.jfa.2007.11.014

M3 - Article

AN - SCOPUS:38649143653

VL - 254

SP - 1161

EP - 1187

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 5

ER -