\(KK\)-theory as the \(K\)-theory of \(C^*\)-categories
type: Item
instance of: scholarly article
title: \(KK\)-theory as the \(K\)-theory of \(C^*\)-categories
zbMATH Open document ID: 0972.19002
author: Tamaz Kandelaki
published in: Homology, Homotopy and Applications
publication date: 2001-02-19T00:00:00Z
full work available at URL: https://eudml.org/doc/225921
full work available at URL: volume2-1.htm
review text: For a separable \(C^*\)-algebra \(A\) and a \(\sigma\)-unital \(C^*\)-algebra \(B\) the author considers an additive \(C^*\)-category \(\text{Rep}(A,B)\) of \(A,B\)-bimodules with morphisms being \(B\)-homomorphisms that commute with the action of \(A\) modulo compacts. He then defines the category \(\text{Rep}(A,B)\) as the universal pseudoabelian \(C^*\)-category of \(\text{Rep}(A,B)\) and proves that Karoubi's topological \(K\)-group \(K^*(\text{Rep}(A,B))\) is isomorphic to \(KK^{*+1}(A,B)\).
Mathematics Subject Classification ID: 19K35
Mathematics Subject Classification ID: 46L89
Mathematics Subject Classification ID: 46M99
zbMATH DE Number: 1550789
zbMATH Keywords: \(C^*\)-category
zbMATH Keywords: \(KK\)-theory
zbMATH Keywords: topological \(K\)-theory
reviewed by: Vladimir M. Manuilov
MaRDI profile type: Publication
DOI: 10.4310/HHA.2000.V2.N1.A10
Recommended article: \(KK\)-theory of \(C^*\)-categories and the analytic assembly map
Recommended article: Q4666817
Recommended article: Equivariant \(KK\)-theory and \(C^*\)-extensions
Recommended article: The KK-theory of fundamental C*-algebras
Recommended article: Q3441469
Recommended article: C* -Categories
Recommended article: \(C^*\)-algebra homomorphisms and \(KK\)-theory
Recommended article: \(C^*\)-categories, groupoid actions, equivariant \(KK\)-theory, and the Baum--Connes conjecture
Recommended article: Q4732606
Recommended article: Q3341417
description: scientific article; zbMATH DE number 1550789