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

Abstract

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.

37 pages

References in corpus (2)

• Tensor products of C(X)-algebras over C(X)
• A connection between multiresolution wavelet theory of scale N and representations of the Cuntz algebra O_N