An enrichment of KK-theory over the category of symmetric spectra

In [6] Higson showed that the formal properties of the Kasparov KK-theory groups are best understood if one regards KK(A,B) for separable C*-algebras A,B as the morphism set of a category KK. In category language the composition and exterior KKproduct give KK the structure of a symmetric monoidal ca...

Authors: Joachim, Michael
Stolz, Stephan
Division/Institute:FB 10: Mathematik und Informatik
Document types:Article
Media types:Text
Publication date:2009
Date of publication on miami:20.08.2009
Modification date:17.04.2015
Source:Münster Journal of Mathematics, 2 (2009), S. 143-182
Edition statement:[Electronic ed.]
DDC Subject:510: Mathematik
License:InC 1.0
Language:English
Format:PDF document
URN:urn:nbn:de:hbz:6-10569461378
Permalink:http://nbn-resolving.de/urn:nbn:de:hbz:6-10569461378
Digital documents:mjm_vol_2_07.pdf

In [6] Higson showed that the formal properties of the Kasparov KK-theory groups are best understood if one regards KK(A,B) for separable C*-algebras A,B as the morphism set of a category KK. In category language the composition and exterior KKproduct give KK the structure of a symmetric monoidal category which is enriched over abelian groups. We show that the enrichment of KK can be lifted to an enrichment over the category of symmetric spectra.