Ideals generated by projections and inductive limit \(C^*\)-algebras
type: Item
instance of: scholarly article
title: Ideals generated by projections and inductive limit \(C^*\)-algebras
zbMATH Open document ID: 1006.46036
author: Cornel Pasnicu
published in: Rocky Mountain Journal of Mathematics
publication date: 2002-07-02T00:00:00Z
full work available at URL: CONT31-3.html
review text: The author introduces two classes of inductive limit \(C^*\)-algebras: \(GAH\)-algebras (generalized \(AH\)-algebras) and its subclass -- strong \(GAH\)-algebras. A necessary and sufficient condition is given for an ideal of a \(GAH\)-algebra to be generated by projections. It is proved that if \[ 0 \to I \to A \to B \to 0 \] is an exact sequence of \(C^*\)-algebras such that \(A\) is a \(GAH\)-algebra then \(A\) has the ideal property (i.e. any ideal is generated by projections) if and only if \(I\) and \(B\) have the ideal property. The lattice of ideals generated by projections of a strong \(GAH\)-algebra and also the partially ordered set of the stably cofinite ideals generated by projections of a strong \(GAH\)-algebra \(A\) are described under an additional assumption on \(A\).
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L99
zbMATH DE Number: 1744065
zbMATH Keywords: \(C^*\)-algebras
zbMATH Keywords: inductive limit
zbMATH Keywords: \(GAH\)-algebras
zbMATH Keywords: ideal property
zbMATH Keywords: generalized \(AH\)-algebras
reviewed by: Sh. A. Ayupov
MaRDI profile type: Publication
OpenAlex ID: W2038811264
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DOI: 10.1216/RMJM/1020171681
description: scientific article; zbMATH DE number 1744065