A new look at KK-theory
type: Item
instance of: scholarly article
title: A new look at KK-theory
zbMATH Open document ID: 0636.55001
DOI: 10.1007/BF00533986
published in: \(K\)-Theory
publication date: 1987-01-01T00:00:00Z
review text: We describe the Kasparov group KK(A,B) as the set of homotopy classes of homomorphisms from an algebra qA associated with A into \({\mathcal K}\otimes B\). The algebra qA consists of `K-theory differential forms' over A. Its construction is dual to that of \(M_ 2(A)\). The analysis of qA and of its interplay with \(M_ 2(A)\) gives the basic results of KK-theory.
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 4036732
zbMATH Keywords: Kasparov product
zbMATH Keywords: Kasparov KK-theory
zbMATH Keywords: \(C^ *\)-algebras
zbMATH Keywords: homotopy classes of homomorphisms
zbMATH Keywords: K-theory differential forms
author: Joachim Cuntz
reviewed by: Joachim Cuntz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4036732