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

Abstract

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.

13 pages

References in corpus (2)

• Principal noncommutative torus bundles
• Moduli spaces of noncommutative instantons: gauging away noncommutative parameters

Cited by in corpus (4)

• T-duality simplifies bulk-boundary correspondence: some higher dimensional cases
• T-duality simplifies bulk-boundary correspondence: the noncommutative case
• Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality
• Nonassociative strict deformation quantization of C*-algebras and nonassociative torus bundles