Some algebraic features of \(\mathbb{Z}_2\)-graded \(KK\)-theory
type: Item
instance of: scholarly article
title: Some algebraic features of \(\mathbb{Z}_2\)-graded \(KK\)-theory
zbMATH Open document ID: 0897.19003
DOI: 10.1023/A:1007787203626
author: Ulrich Haag
published in: \(K\)-Theory
publication date: 1998-06-11T00:00:00Z
review text: The aim of this article is to study the connection of the author's version of Kasparov's \(\mathbb{Z}_2\)-graded \(KK\)-functor and the graded Kasparov's Ext-functor. One of the main results is a new construction of the Kasparov product for the graded \(KK\)-functor. The generalizations to \(\mathbb{Z}_2\)-graded \(C^*\)-algebras of the universal coefficient theorem, the Künneth theorems for \(KK_* (A,B)\) and \(K_* (A\otimes B)\), and the Thom isomorphism theorem are obtained. The methods of this paper are closely connected with Cuntz's approach in the ungraded case.
Mathematics Subject Classification ID: 19K35
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 1132938
zbMATH Keywords: \(KK\)-theory
zbMATH Keywords: \(\mathbb{Z}_2\)-graded \(C^*\)-algebras
zbMATH Keywords: Kasparov product
zbMATH Keywords: Künneth theorems
reviewed by: V. M. Deundjak
MaRDI profile type: Publication
full work available at URL: a:1007787203626
OpenAlex ID: W2053289803
description: scientific article; zbMATH DE number 1132938