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

K. C. Hannabuss; V. Mathai

doi:10.1017/S1446788711001170

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

Quantum Algebra 2011-08-19 v2 High Energy Physics - Theory Differential Geometry

Authors: K. C. Hannabuss , V. Mathai

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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.

Keywords

hilbert modules deformation theory c*-algebra

Cite

@article{arxiv.1007.4696,
  title  = {Parametrised strict deformation quantization of C*-bundles and Hilbert C*-modules},
  author = {K. C. Hannabuss and V. Mathai},
  journal= {arXiv preprint arXiv:1007.4696},
  year   = {2011}
}

Comments

13 pages