TY - JOUR
T1 - Equivariance and imprimivity for discrete hopf c*-coactions
AU - Kaliszewski, Steven
AU - Quigg, John
PY - 2000/10
Y1 - 2000/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0040786722&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0040786722&partnerID=8YFLogxK
U2 - 10.1017/S0004972700018736
DO - 10.1017/S0004972700018736
M3 - Article
AN - SCOPUS:0040786722
SN - 0004-9727
VL - 62
SP - 253
EP - 272
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 2
ER -