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

TL;DR

This paper extends the theory of parametrised strict deformation quantization of C*-bundles, providing new examples, applications, and a framework for deforming Hilbert C*-modules and monoidal categories, with implications for noncommutative geometry.

Contribution

It introduces a method to deform Hilbert C*-modules over C*-bundles with torus actions, expanding the scope of deformation quantization techniques.

Findings

Classified H_3-twisted noncommutative torus bundles over spaces.

Extended deformation techniques to general torus bundles.

Deformed monoidal categories and modules using Rieffel's construction.

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.