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Type: Journal article
Title: Parameterized strict deformation quantization of C*-bundles and Hilbert C*-modules
Author: Hannabuss, K.
Varghese, M.
Citation: Journal of the Australian Mathematical Society, 2011; 90(1):25-38
Publisher: Australian Mathematics Publ Assoc Inc
Issue Date: 2011
ISSN: 1446-7887
Statement of
Keith C. Hannabuss and Varghese Mathai
Abstract: In this paper, we review the parametrized strict deformation quantization of C*-bundles obtained in a previous paper, and give more examples and applications of this theory. In particular, it is used here to classify H3-twisted noncommutative torus bundles over a locally compact space. This is extended to the case of general torus bundles and their parametrized strict deformation quantization. Rieffel’s basic construction of an algebra deformation can be mimicked to deform a monoidal category, which deforms not only algebras but also modules. As a special case, we consider the parametrized strict deformation quantization of Hilbert C*-modules over C*-bundles with fibrewise torus action.
Keywords: parametrized strict deformation quantization; noncommutative principal torusbundles; T -duality, Hilbert module categories
Rights: © Cambridge University Press 2011
RMID: 0020110497
DOI: 10.1017/S1446788711001170
Appears in Collections:Mathematical Sciences publications

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