TY - JOUR
T1 - Induced coactions of discrete groups on C *-algebras
AU - Echterhoff, Siegfried
AU - Quigg, John
PY - 1999/8
Y1 - 1999/8
N2 - Using the close relationship between coactions of discrete groups and Fell bundles, we introduce a rocedure for inducing a C*-coaction δ: D → D ⊗ C* (G/N) of a quotient group G/N of a discrete group G to a C*-coaction Ind δ: Ind D → Ind D ⊗ C* (G) of G. We show that induced coactions behave in many respects similarly to induced actions. In particular, as an analogue of the well known imprimitivity theorem for induced actions we prove that the crossed products Ind D ×Ind δ G and D ×δ G/N are always Morita equivalent. We also obtain nonabelian analogues of a theorem of Diesen and Pedersen which show that there is a duality between induced coactions and twisted actions in the sense of Green. We further investigate amenability of Fell bundles corresponding to induced coactions.
AB - Using the close relationship between coactions of discrete groups and Fell bundles, we introduce a rocedure for inducing a C*-coaction δ: D → D ⊗ C* (G/N) of a quotient group G/N of a discrete group G to a C*-coaction Ind δ: Ind D → Ind D ⊗ C* (G) of G. We show that induced coactions behave in many respects similarly to induced actions. In particular, as an analogue of the well known imprimitivity theorem for induced actions we prove that the crossed products Ind D ×Ind δ G and D ×δ G/N are always Morita equivalent. We also obtain nonabelian analogues of a theorem of Diesen and Pedersen which show that there is a duality between induced coactions and twisted actions in the sense of Green. We further investigate amenability of Fell bundles corresponding to induced coactions.
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U2 - 10.4153/CJM-1999-032-1
DO - 10.4153/CJM-1999-032-1
M3 - Article
AN - SCOPUS:0033439210
SN - 0008-414X
VL - 51
SP - 745
EP - 770
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
IS - 4
ER -