Full duality for coactions of discrete groups

  • Siegfried Echterhoff
  • John Quigg

Abstract

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.
Published
2002-06-01
How to Cite
Echterhoff, S., & Quigg, J. (2002). Full duality for coactions of discrete groups. MATHEMATICA SCANDINAVICA, 90(2), 267-288. https://doi.org/10.7146/math.scand.a-14374
Section
Articles