Induced coactions of discrete groups on C*-algebras

Details Induced coactions of discrete groups on C*-algebras Induced coactions of discrete groups on C*-algebras

1998-01-13

arxiv.org/abs/math/9801069v1

Mathematics

Operator Algebras

26 pages, Latex

Scientific paper

Using the close relationship between coactions of discrete groups and Fell bundles, we introduce a procedure for inducing a C*-coaction of a quotient group G/N of a discrete group G to a C*-coaction of G itself on an induced C*-algebra. 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 of the original and the induced coactions are always Morita equivalent. We also obtain nonabelian analogues of a theorem of Olesen 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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