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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
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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

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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