## Abstract

Let U, V, and W be multiplicative unitaries coming from discrete Kac systems such that W is an amenable normal submultiplicative unitary of V with quotient U. We define notions for right-Hilbert bimodules of coactions of S_{V} and Ŝ_{V}, their restrictions to S_{W} and Ŝ_{U}, their dual coactions, and their full and reduced crossed products. If N(A) denotes the imprimitivity bimodule associated to a coaction δ of S_{V} on a C*-algebra A by Ng's imprimitivity theorem, we prove that for a suitably nondegenerate injective right-Hilbert bimodule coaction of S_{V} on _{A}X_{B}, the balanced tensor products N(A) ⊗ _{A × ŜW} (_{A}X_{B} × Ŝ_{W}) and (_{A}X_{B} × Ŝ_{V} x_{r} S_{U}) ⊗ _{B × ŜV xrSU} N(B) are isomorphic right-Hilbert A × Ŝ_{V} xr S_{U} - B × Ŝ_{W} bimodules. This can be interpreted as a natural equivalence between certain crossed-product functors.

Original language | English (US) |
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Pages (from-to) | 253-272 |

Number of pages | 20 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 62 |

Issue number | 2 |

DOIs | |

State | Published - Oct 2000 |

## ASJC Scopus subject areas

- Mathematics(all)