Classification of certain infinite simple \(C^*\)-algebras
type: Item
instance of: scholarly article
title: Classification of certain infinite simple \(C^*\)-algebras
zbMATH Open document ID: 0831.46063
author: Mikael Rørdam
published in: Journal of Functional Analysis
publication date: 1996-02-18T00:00:00Z
review text: The author shows that the class of \(C^*\)-algebras, that arise as the crossed product of a stable simple AF-algebra with a \(\mathbb{Z}\)-action determined by an automorphism, which maps a projection in the algebra onto a proper subprojection, consists of simple, purely infinite \(C^*\)- algebras, and he shows that a specific subclass of it is classified by \(K\)-theory. This subclass is large enough to exhaust all possible \(K\)- groups: if \(G_0\) and \(G_1\) are countable abelian groups, with \(G_1\) torsion free (as it must be), then there is a \(C^*\)-algebra \(A\) in the classified subclass with \(K_0(A)\cong G_0\) and \(K_1(A)\cong G_1\). The subclass contains the Cuntz algebras \({\mathcal O}_n\), with \(n\) even, and the Cuntz-Krieger algebras \({\mathcal O}_A\), with \(K_0({\mathcal O}_A)\) of finite odd order, and it is closed under forming inductive limits. The \(C^*\)-algebras in the classified subclass can be viewed as classifiable models (in a strong sense) of general, simple purely infinite \(C^*\)-algebras with the same \(K\)-theory.
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 790370
zbMATH Keywords: crossed product of a stable simple AF-algebra with a \(\mathbb{Z}\)-action
zbMATH Keywords: simple, purely infinite \(C^*\)-algebras
zbMATH Keywords: Cuntz algebras
zbMATH Keywords: Cuntz-Krieger algebras
MaRDI profile type: Publication
full work available at URL: jfan.1995.1095
OpenAlex ID: W2069423814
DOI: 10.1006/JFAN.1995.1095
description: scientific article; zbMATH DE number 790370