Classification of simple \(C^*\)-algebras: Inductive limits of matrix algebras over one-dimensional spaces
type: Item
instance of: scholarly article
title: Classification of simple \(C^*\)-algebras: Inductive limits of matrix algebras over one-dimensional spaces
zbMATH Open document ID: 1034.46058
author: Liangqing Li
published in: Journal of Functional Analysis
publication date: 2002-09-08T00:00:00Z
review text: The aim of this paper is the classification of simple \(C^*\)-algebras which can be written as inductive limits of algebras of the form \(A_{n} = \bigoplus_{i=1}^{K_{n}} M_{[n,i]} (C(X_{n,i}))\), where \(X_{n,i}\) is an arbitrary one-dimensional compact metrizable space. This result continues with the classification of simple \(C^*\)-algebras started by \textit{G. Elliott}. The author generalizes previously known results for the case \(X_{n,i}=S^{1}\) and for the case \(X_{n,i}\) being trees and is able to reduce the case of general one-dimensional spaces to circles. The strategies for the proof developed by the author are very technical and of a great interest.
Mathematics Subject Classification ID: 46L35
zbMATH DE Number: 1797594
zbMATH Keywords: simple \(C^*\)-algebras
zbMATH Keywords: inductive limits
reviewed by: Antonio M. Peralta
MaRDI profile type: Publication
full work available at URL: jfan.2002.3895
OpenAlex ID: W1963790637
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DOI: 10.1006/JFAN.2002.3895
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description: scientific article; zbMATH DE number 1797594