On the homotopy type of the unitary group and the Grassmann space of purely infinite simple \(C^*\)-algebras
type: Item
instance of: scholarly article
title: On the homotopy type of the unitary group and the Grassmann space of purely infinite simple \(C^*\)-algebras
zbMATH Open document ID: 1014.46035
DOI: 10.1023/A:1013392615189
author: Shuang Zhang
published in: \(K\)-Theory
publication date: 2003-07-21T00:00:00Z
review text: The paper provides some topological information about purely infinite simple \(C^*\)-algebras in terms of \(K\)-theory. Let \(A\) be one such algebra and \(\widetilde A\) be its unitalization. It is shown that the homotopy groups of the unitary group and the space of projections of \(\widetilde A\) are isomorphic to either \(K_0(A)\) or \(K_1(A)\). It follows from this that \(K_0(A)= K_1(A)=0\) if and only if the unitary group of \(\widetilde A\) is a contractible topological space. The same results are also true if \(\widetilde A\) is replaced by the associated generalized Calkin algebra.
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 1749306
zbMATH Keywords: \(K\)-theory
zbMATH Keywords: Calkin algebra
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
full work available at URL: a:1013392615189
OpenAlex ID: W2039093332
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description: scientific article; zbMATH DE number 1749306