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

Takeshi Katsura

doi:10.1016/j.jfa.2007.11.014

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

Takeshi Katsura

Research output: Contribution to journal › Article › peer-review

38 Citations (Scopus)

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	https://doi.org/10.1016/j.jfa.2007.11.014
Publication status	Published - 2008 Mar 1
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/j.jfa.2007.11.014

Cite this

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

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.",

keywords = "C-algebra, Dynamical system, Graph algebra, Homeomorphism C-algebra, K-theory, Kirchberg algebra, Purely infinite, Topological graph",

author = "Takeshi Katsura",

note = "Funding Information: * Address for correspondence: The Fields Institute for Research in Mathematical Sciences, 222 College Street, Second Floor, Toronto, Ontario, Canada. E-mail address: katsura@math.sci.hokudai.ac.jp. 1 The author is partially supported by Research Fellowship for Young Scientists of the Japan Society for the Promotion of Science.",

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AU - Katsura, Takeshi

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PY - 2008/3/1

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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

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