KK-theory of reduced free-product \(C^*\)-algebras
type: Item
instance of: scholarly article
title: KK-theory of reduced free-product \(C^*\)-algebras
zbMATH Open document ID: 0863.46046
DOI: 10.1215/S0012-7094-96-08229-0
author: Emmanuel Germain
published in: Duke Mathematical Journal
publication date: 1997-06-03T00:00:00Z
review text: Let \(A_r\) denote the reduced free-product \(C^*\)-algebra of a set of \(K\)-nuclear \(C^*\)-algebras endowed with states, and let \(A\) be the full free-product \(C^*\)-algebra. One of the purposes of this paper is to get a candidate for the inverse in \(KK(A_r,A)\) of the canonical morphism from \(A\) to \(A_r\) and to show that this morphism always realizes a so named \(K\)-theoretical equivalence. The tools developed here allow to give a unified treatment and to extend to a larger set of \(C^*\)-algebras the computation of the \(KK\)-groups of full free-product \(C^*\)-algebras. To this purpose the notion of \(K\)-pointed \(C^*\)-algebra is introduced and the main properties of such \(C^*\)-algebras are considered.
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 19K35
zbMATH DE Number: 908707
zbMATH Keywords: \(KK\)-theory
zbMATH Keywords: reduced free-product \(C^*\)-algebra
zbMATH Keywords: \(K\)-nuclear \(C^*\)-algebras
zbMATH Keywords: states
zbMATH Keywords: \(K\)-theoretical equivalence
zbMATH Keywords: \(KK\)-groups
zbMATH Keywords: \(K\)-pointed \(C^*\)-algebra
reviewed by: V. M. Deundjak
MaRDI profile type: Publication
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full work available at URL: s0012-7094-96-08229-0
OpenAlex ID: W2071830724
description: scientific article; zbMATH DE number 908707