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Three Bimodules for Mansfield's Imprimitivity Theorem

2000/02/04 by S. Kaliszewski, John Quigg, Kaliszewski, S. +1
Mathematics · #46L55 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/0002038

LaTeX-2e, 20 pages, uses packages amssymb, xy, upref

arxiv created 2000/02/04 · openalex publication_date 2000/02/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 crossed-product 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.

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