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ON THE CLASSIFICATION OF NUCLEAR C*-ALGEBRAS

Published online by Cambridge University Press:  09 July 2002

MARIUS DADARLAT  and
SØREN EILERS
MARIUS DADARLAT
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA. [email protected]
SØREN EILERS
Affiliation:
Matematisk Afdeling, Københavns Universitet, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark. [email protected]
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Abstract

We employ results from KK-theory, along with quasidiagonality techniques, to obtain wide-ranging classification results for nuclear C*-algebras. Using a new realization of the Cuntz picture of the Kasparov groups we show that two morphisms inducing equal KK-elements are approximately stably unitarily equivalent. Using K-theory with coefficients to associate a partial KK-element to an approximate morphism, our result is generalized to cover such maps. Conversely, we study the problem of lifting a (positive) partial KK-element to an approximate morphism. These results are employed to obtain classification results for certain classes of quasidiagonal C*-algebras introduced by H. Lin, and to reprove the classification of purely infinite simple nuclear C*-algebras of Kirchberg and Phillips. It is our hope that this work can be the starting point of a unified approach to the classification of nuclear C*-algebras.

2000 Mathematical Subject Classification: primary 46L35; secondary 19K14, 19K35, 46L80.

Keywords

nuclear C*-algebrasclassificationK-theoryKK-theoryquasidiagonality
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 85 , Issue 1 , March 2002 , pp. 168 - 210
Copyright
2002 London Mathematical Society

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