\(C^*\)-algèbres de Hopf et théorie de Kasparov équivariante. (Hopf \(C^*\)-algebras and equivariant Kasparov theory)
type: Item
instance of: scholarly article
title: \(C^*\)-algèbres de Hopf et théorie de Kasparov équivariante. (Hopf \(C^*\)-algebras and equivariant Kasparov theory)
zbMATH Open document ID: 0683.46048
DOI: 10.1007/BF00538428
author: Saad Baaj
author: Georges Skandalis
published in: \(K\)-Theory
publication date: 1989-01-01T00:00:00Z
review text: The authors define a concept of coaction of a Hopf \(C^*\)-algebra S on a pair of \(C^*\)-algebras (A,B) and generalise for the triple of the type (S,A,B) the Kasparov construction corresponding to the case of \(S=C_ 0(G)\), G being a locally compact group. So, an S-equivariant Kasparov theory group \(KK_ S(A,B)\) is obtained. Moreover, the Kasparov product is generalised to that setting, a natural isomorphism of the groups \(KK_ G(A,B)\) and \(KK_{C^*(G)}(A\times G,B\times G)\) is given and, for a discrete amenable group \(\Gamma\), the half-exactness of the functors \(KK_{\Gamma}(.,D)\) and \(KK_{\Gamma}(D,.)\) is proved.
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 4119008
zbMATH Keywords: coaction of a Hopf \(C^*\)-algebra
zbMATH Keywords: Kasparov construction
zbMATH Keywords: S-equivariant Kasparov theory group
zbMATH Keywords: Kasparov product
zbMATH Keywords: discrete amenable group
zbMATH Keywords: half- exactness
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4119008