Three Bimodules for Mansfield's Imprimitivity Theorem
Abstract
There are at least three imprimitivity bimodules naturally associated to a maximal coaction of a discrete group G on a C*algebra and a normal subgroup of G: Mansfield's bimodule; the bimodule assembled by Ng from Green's imprimitivity bimodule and Katayama duality; and a bimodule assembled from Green's bimodule and a crossedproduct Mansfield bimodule. We show that all three of these are isomorphic, so that the corresponding inducing maps on representations are identical. This can be interpreted as saying that Mansfield and Green induction are inverses of one another ``modulo Katayama duality''. These results pass to twisted coactions; dual results starting with an action are also given.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2000
 arXiv:
 arXiv:math/0002038
 Bibcode:
 2000math......2038K
 Keywords:

 Operator Algebras;
 46L55
 EPrint:
 LaTeX2e, 20 pages, uses packages amssymb, xy, upref