A classification of simple limits of splitting interval algebras
type: Item
instance of: scholarly article
title: A classification of simple limits of splitting interval algebras
zbMATH Open document ID: 0921.46057
author: Xinhui Jiang
author: Hongbing Su
published in: Journal of Functional Analysis
publication date: 1999-09-17T00:00:00Z
review text: Splitting interval algebras take the form \(\{f\in M_n(C[0,1]):f(0)\in\oplus M_{p_i},\;f(1)\in\oplus M_{q_j}\}\) where the \(\{p_i\}\) and \(\{q_j\}\) each sum to \(n\). The main theorem of the paper classifies simple unital inductive limits of finite direct sums of such algebras in terms of scaled ordered groups and tracial state spaces. This fits into \textit{G. Elliott}'s classification program for amenable \(C^*\)-algebras as surveyed in [Proceedings of the international congress of mathematicians, ICM '94, August 3-11, 1994, Zürich, Switzerland. Vol. II. Basel: Birkhäuser, 922-932 (1995)].
Mathematics Subject Classification ID: 46L35
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 1106589
zbMATH Keywords: Riesz decomposition property
zbMATH Keywords: simple limits of splitting interval algebras
zbMATH Keywords: classification
zbMATH Keywords: amenable \(C^*\)-algebras
reviewed by: Edward A. Azoff
MaRDI profile type: Publication
full work available at URL: jfan.1997.3120
OpenAlex ID: W2074661453
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DOI: 10.1006/JFAN.1997.3120
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description: scientific article; zbMATH DE number 1106589