Induced coactions of discrete groups on C *-algebras

Siegfried Echterhoff, John Quigg

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)745-770
Number of pages26
JournalCanadian Journal of Mathematics
Volume51
Issue number4
DOIs
StatePublished - Aug 1999

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ASJC Scopus subject areas

  • Mathematics(all)

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