The C*-algebra of a vector bundle and fields of Cuntz algebras
Operator Algebras
2011-11-18 v2 K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.math/0404166,
title = {The C*-algebra of a vector bundle and fields of Cuntz algebras},
author = {Ezio Vasselli},
journal= {arXiv preprint arXiv:math/0404166},
year = {2011}
}
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37 pages