Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T12:35:30.791Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on Kasparov products

Published online by Cambridge University Press:  24 January 2012

Martin Grensing
Martin Grensing*
Affiliation:
Université Denis-Diderot - Paris 7, Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, 75 013 Parisgrensing@gmx.net
Get access

Abstract

Combining Kasparov's generalization of a theorem of Voiculescu and Cuntz's description of KK-theory in terms of quasihomomorphisms (sections one and two), we give a simple construction of the Kasparov product (section three). This construction will be generalized in [Gre] to give a version of the product for so-called locally convex Kasparov modules over locally convex algebras in order to treat products of certain universal cycles.

Keywords

Bivariant K-theoryKasparov productquasihomomorphism
Type
Research Article
Information
Journal of K-Theory , Volume 10 , Issue 2 , October 2012 , pp. 233 - 240
Copyright
Copyright © ISOPP 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

CS84.Connes, A. and Skandalis, G.. The longitudinal index theorem for foliations. Publ. Res. Inst. Math. Sci. 20(6): 1139–1183, 1984.Google Scholar
Cun83.Cuntz, J.. Generalized homomorphisms between C*-algebras and KK-theory. In Dynamics and processes (Bielefeld, 1981), Lecture Notes in Math. 1031, 31–45. Springer, Berlin, 1983.Google Scholar
Cun87.Cuntz, J.. A new look at KK-theory. K-Theory 1(1):31–51, 1987.Google Scholar
Gre.Grensing, M.. Universal cycles and homological invariants of locally convex algebras. arXiv:1103.6243v1, submitted for publication to the Journal of Functional Analysis.Google Scholar
Kas80a.Kasparov, G. G.. Hilbert C*-modules: theorems of Stinespring and Voiculescu. J. Operator Theory 4(1):133–150, 1980.Google Scholar
Kas80b.Kasparov, G. G.. The operator K-functor and extensions of C*-algebras. Izv. Akad. Nauk SSSR Ser. Mat. 44(3):571–636, 719, 1980.Google Scholar
Ska84.Skandalis, G.. Some remarks on Kasparov theory. J. Funct. Anal. 56(3):337–347, 1984.Google Scholar
Ska88.Skandalis, G.. Une notion de nucléarité en K-théorie (d'après J. Cuntz). K-Theory 1(6):549–573, 1988.Google Scholar
Tho01.Thomsen, K.. On absorbing extensions. Proc. Amer. Math. Soc. 129(5):1409–1417 (electronic), 2001.Google Scholar