Approximately unitarily equivalent morphisms and inductive limit \(C^*\)- algebras
type: Item
instance of: scholarly article
title: Approximately unitarily equivalent morphisms and inductive limit \(C^*\)- algebras
zbMATH Open document ID: 0828.46055
DOI: 10.1007/BF00961456
published in: \(K\)-Theory
publication date: 1995-09-11T00:00:00Z
review text: Let \({\mathcal A}\) denote a simple \(C^*\)-algebra of real rank zero which is an inductive limit of homogeneous algebras whose spectra are finite CW complexes of uniformly bounded (or slowly growing) dimension and torsion free \(K^0\)-group. Using the Connes-Higson theory of asymptotic morphisms, the author shows that \({\mathcal A}\) falls into the class of simple \(C^*\)-algebras of real rank zero that are classified by their graded order-unit \(K\)-groups. This extends previous work by \textit{G. A. Elliott} [J. Reine Angew. Math. 443, 179-219 (1993; Zbl 0809.46067)] and Elliott and \textit{G. Gong} (to appear).
Mathematics Subject Classification ID: 46L35
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 19K14
zbMATH DE Number: 784416
zbMATH Keywords: simple \(C^*\)-algebra of real rank zero
zbMATH Keywords: inductive limit of homogeneous algebras whose spectra are finite CW complexes
zbMATH Keywords: torsion free \(K^ 0\)- group
zbMATH Keywords: Connes-Higson theory of asymptotic morphisms
zbMATH Keywords: graded order-unit \(K\)-groups
author: Marius Dadarlat
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00961456
OpenAlex ID: W2054593812
description: scientific article; zbMATH DE number 784416