The C*-algebra of a vector bundle and fields of Cuntz algebras

Details The C*-algebra of a vector bundle and fields of Cuntz algebras The C*-algebra of a vector bundle and fields of Cuntz algebras

2004-04-07

arxiv.org/abs/math/0404166v2

Journal of Functional Analysis 222(2) (2005), 491-502

Mathematics

Operator Algebras

37 pages

Scientific paper

We study the Pimsner algebra associated with the module of continuous sections of a Hilbert bundle, and prove that it is a continuous bundle of Cuntz algebras. We discuss the role of such Pimsner algebras w.r.t. the notion of inner endomorphism. Furthermore, we study bundles of Cuntz algebras carrying a global circle action, and assign to them a class in the representable KK-group of the zero-grade bundle. We compute such class for the Pimsner algebra of a vector bundle.

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