Equivariance and imprimivity for discrete hopf c*-coactions

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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 SV and ŜV, their restrictions to SW and ŜU, their dual coactions, and their full and reduced crossed products. If N(A) denotes the imprimitivity bimodule associated to a coaction δ of SV on a C*-algebra A by Ng's imprimitivity theorem, we prove that for a suitably nondegenerate injective right-Hilbert bimodule coaction of SV on AXB, the balanced tensor products N(A) ⊗ A × ŜW (AXB × ŜW) and (AXB × ŜV xr SU) ⊗ B × ŜV xrSU N(B) are isomorphic right-Hilbert A × ŜV xr SU - B × ŜW bimodules. This can be interpreted as a natural equivalence between certain crossed-product functors.

Original languageEnglish (US)
Pages (from-to)253-272
Number of pages20
JournalBulletin of the Australian Mathematical Society
Issue number2
StatePublished - Oct 2000

ASJC Scopus subject areas

  • General Mathematics


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