2006 | OriginalPaper | Buchkapitel
Bundles of C*-algebras and the KK(X;−,−)-bifunctor
verfasst von : Ezio Vasselli
Erschienen in: C*-algebras and Elliptic Theory
Verlag: Birkhäuser Basel
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An overview about
C
*-algebra bundles with a ℤ-grading is presented, with particular emphasis on classification questions. In particular, we discuss the role of the representable
KK
(
X
;−,−)-bifunctor introduced by Kasparov. As an application, we consider Cuntz-Pimsner algebras associated with vector bundles, and give a classification in terms of
K
-theoretical invariants in the case in which the base space is an
n
-sphere.