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PARAMETRIZED STRICT DEFORMATION QUANTIZATION OF C*-BUNDLES AND HILBERT C*-MODULES

Part of: Selfadjoint operator algebras Infinite-dimensional manifolds Symplectic geometry, contact geometry Modules, bimodules and ideals

Published online by Cambridge University Press:  18 May 2011

KEITH C. HANNABUSS  and
VARGHESE MATHAI
KEITH C. HANNABUSS
Affiliation:
Mathematical Institute, 24–29 St. Giles’, Oxford OX1 3LB, England Balliol College, Oxford OX1 3BJ, England (email: kch@balliol.ox.ac.uk)
VARGHESE MATHAI*
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide SA 5005, Australia (email: mathai.varghese@adelaide.edu.au)
*
✉For correspondence; e-mail: mathai.varghese@adelaide.edu.au
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Abstract

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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 quantizationnoncommutative principal torus bundlesT-dualityHilbert module categories

MSC classification

Secondary: 58B34: Noncommutative geometry (à la Connes) 46L87: Noncommutative differential geometry 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality 53D55: Deformation quantization, star products
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 90 , Issue 1 , February 2011 , pp. 25 - 38
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The second author was supported by the Australian Research Council.

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