Parametrised strict deformation quantization of C*-bundles and Hilbert C*-modules

In this paper, we use the parametrised 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 H_3-twisted noncommutative torus bundles over a locally compact space. This is extended to the case of general torus bundles and their parametrised 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 parametrised strict deformation quantization of Hilbert C*-modules over C*-bundles with fibrewise torus action.

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$C^{*}$ -Algebras in Tensor Categories

Peter Bouwknegt
(
- Australian Natl. U., Canberra
)
,
Keith C. Hannabuss
(
- Oxford U., Inst. Math. and
- Oxford U.
)
,
Varghese Mathai
(
- Adelaide U.
)

- Clay Math.Proc. 12 (2010) 127-166
•
e-Print:
- math/0702802

C* algebras and differential geometry

Alain Connes

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e-Print:
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- Adv.Math. 39 31

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Noncommutative principal torus bundles via parametrised strict deformation quantization

- Proc.Symp.Pure Math. 81 (2010) 133-148,
- AMS Proceedings of Symposia in Pure Mathematics 81 (2010) 133-148
•
e-Print:
- 0911.1886
•
DOI:
- 10.1090/pspum/081/2681761