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.
ASJC Scopus subject areas
- General Mathematics