Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras

Sara E. Arklint; Rasmus Bentmann; Takeshi Katsura

doi:10.1017/is014009013jkt281

Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras

Sara E. Arklint, Rasmus Bentmann, Takeshi Katsura

Department of Mathematics

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

7 Citations (Scopus)

Abstract

We show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C∗-algebras with certain primitive ideal spaces - including the infinitely many so-called accordion spaces for which filtered K-theory is known to be a complete invariant. As a consequence, we give a characterization of purely infinite Cuntz-Krieger algebras whose primitive ideal space is an accordion space.

Original language	English
Pages (from-to)	570-613
Number of pages	44
Journal	Journal of K-Theory
Volume	14
Issue number	3
DOIs	https://doi.org/10.1017/is014009013jkt281
Publication status	Published - 2014 Jul 8

Keywords

C∗-algebras
classification
filtered K-theory
graph C∗-algebras
real rank zero

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.1017/is014009013jkt281

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title = "Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras",

abstract = "We show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C∗-algebras with certain primitive ideal spaces - including the infinitely many so-called accordion spaces for which filtered K-theory is known to be a complete invariant. As a consequence, we give a characterization of purely infinite Cuntz-Krieger algebras whose primitive ideal space is an accordion space.",

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AU - Arklint, Sara E.

AU - Bentmann, Rasmus

AU - Katsura, Takeshi

N1 - Funding Information: This research was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92). The third-named author was partially supported by the Japan Society for the Promotion of Science. Publisher Copyright: Copyright © ISOPP 2014.

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N2 - We show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C∗-algebras with certain primitive ideal spaces - including the infinitely many so-called accordion spaces for which filtered K-theory is known to be a complete invariant. As a consequence, we give a characterization of purely infinite Cuntz-Krieger algebras whose primitive ideal space is an accordion space.

AB - We show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C∗-algebras with certain primitive ideal spaces - including the infinitely many so-called accordion spaces for which filtered K-theory is known to be a complete invariant. As a consequence, we give a characterization of purely infinite Cuntz-Krieger algebras whose primitive ideal space is an accordion space.

KW - C∗-algebras

KW - classification

KW - filtered K-theory

KW - graph C∗-algebras

KW - real rank zero

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Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras

Abstract

Keywords

ASJC Scopus subject areas

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