Sur la simplicité essentielle du groupe des inversibles et du groupe unitaire dans une \(C^*\)-algèbre simple
type: Item
instance of: scholarly article
title: Sur la simplicité essentielle du groupe des inversibles et du groupe unitaire dans une \(C^*\)-algèbre simple
zbMATH Open document ID: 0573.46033
DOI: 10.1016/0022-1236(85)90010-2
author: Pierre de la Harpe
author: Georges Skandalis
published in: Journal of Functional Analysis
publication date: 1985-01-01T00:00:00Z
review text: Let A be a simple approximately finite-dimensional \(C^*\)-algebra with unit, let \(GL_ 1(A)\) be the group of invertible elements and let \(U_ 1(A)\) be that of unitaries in A. In a previous work the abelianized groups \(GL_ 1(A)/DGL_ 1(A)\) and \(U_ 1(A)/DU_ 1(A)\) have been described with Grothendieck's group \(K_ 0(A)\) viewed as a dimension group for A [See Ann. Inst. Fourier 34, No.1, 241-260 and No.4, 169-202 (1984; Zbl 0534.46036 and Zbl 0548.46044)]. Here, it is shown that the groups \(DGL_ 1(A)\) and \(DU_ 1(A)\) are simple up to their centres. There are K-theoretic corollaries.
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L40
Mathematics Subject Classification ID: 46M20
zbMATH DE Number: 3914994
zbMATH Keywords: approximately finite-dimensional \(C^*\)-algebra with unit
zbMATH Keywords: group of invertible elements
zbMATH Keywords: Grothendieck's group
zbMATH Keywords: dimension group
MaRDI profile type: Publication
full work available at URL: 0022-1236(85)90010-2
OpenAlex ID: W2042176218
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description: scientific article; zbMATH DE number 3914994