TY - JOUR

T1 - Full duality for coactions of discrete groups

AU - Echterhoff, Siegfried

AU - Quigg, John

PY - 2002/1/1

Y1 - 2002/1/1

N2 - Using the strong relation between coactions of a discrete group G on C*-algebras and Fell bundles over G we prove a new version of Mansfield's imprimitivity theorem for coactions of discrete groups. Our imprimitivity theorem works for the universally defined full crossed products and arbitrary subgroups of G as opposed to the usual theory of [16], [11] which uses the spatially defined reduced crossed products and normal subgroups of G. Moreover, our theorem factors through the usual one by passing to appropriate quotients. As applications we show that a Fell bundle over a discrete group is amenable in the sense of Exel [7] if and only if the double dual action is amenable in the sense that the maximal and reduced crossed products coincide. We also give a new characterization of induced coactions in terms of their dual actions.

AB - Using the strong relation between coactions of a discrete group G on C*-algebras and Fell bundles over G we prove a new version of Mansfield's imprimitivity theorem for coactions of discrete groups. Our imprimitivity theorem works for the universally defined full crossed products and arbitrary subgroups of G as opposed to the usual theory of [16], [11] which uses the spatially defined reduced crossed products and normal subgroups of G. Moreover, our theorem factors through the usual one by passing to appropriate quotients. As applications we show that a Fell bundle over a discrete group is amenable in the sense of Exel [7] if and only if the double dual action is amenable in the sense that the maximal and reduced crossed products coincide. We also give a new characterization of induced coactions in terms of their dual actions.

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U2 - 10.7146/math.scand.a-14374

DO - 10.7146/math.scand.a-14374

M3 - Article

AN - SCOPUS:0036326908

VL - 90

SP - 267

EP - 288

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

SN - 0025-5521

IS - 2

ER -