Classification of certain infinite simple \(C^*\)-algebras. II
type: Item
instance of: scholarly article
title: Classification of certain infinite simple \(C^*\)-algebras. II
zbMATH Open document ID: 0864.46038
DOI: 10.1007/BF02566025
author: Mikael Rørdam
author: George A. Elliott
published in: Commentarii Mathematici Helvetici
publication date: 1997-06-26T00:00:00Z
full work available at URL: https://eudml.org/doc/140385
review text: The follow-up of a paper (with the same title) by the second named author [J. Funct. Anal. 131, No. 2, 415-458 (1995; Zbl 0831.46063)], the construction of classifiable models of separable, purely infinite, simple \(C^*\)-algebras is completed. Algebras in this class of classifiable models are completely determined (up to isomorphism) by the triple \((K_0{\mathcal A}),[1],K_1({\mathcal A})\)) for \(\mathcal A\) unital and by the \(K\)-groups alone for \(\mathcal A\) non-unital. The author gives a necessary and sufficient condition for a \(C^*\)-algebra \(\mathcal A\) to have a model \(C^*\)-algebra \({\mathcal A}_0\) in this class with the same triple (or the same \(K\)-groups in the non-unital case). Moreover, any triple \((G_0,g_0,G_1)\) with \(G_0\), \(G_1\) countable Abelian groups, \(g_0\in G_0\), can be realized in this way; the condition that \(G_1\) has to be torsionfree could now be removed.
Mathematics Subject Classification ID: 46L35
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 852030
zbMATH Keywords: classifiable models of separable, purely infinite, simple \(C^*\)-algebras
MaRDI profile type: Publication
OpenAlex ID: W2072964319
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description: scientific article; zbMATH DE number 852030