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

  • Part of
  • KEITH C. HANNABUSS, VARGHESE MATHAI
  • Journal:
    Journal of the Australian Mathematical Society / Volume 90 / Issue 1 / February 2011
    Published online by Cambridge University Press:
    18 May 2011, pp. 25-38
    Print publication:
    February 2011
    • Article
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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.