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On Ng's Proof of Mansfield's Imprimitivity Theorem
by
S. Kaliszewski
Arizona State University
Coauthors: John Quigg (Arizona State University)
C. K. Ng has observed that an abstract Morita equivalence between a restricted coaction crossed product A ×\delta G/N and the iterated dual action crossed product A ×\delta G ×[^(\delta)] N can be pieced together from Green's imprimitivity theorem and Katayama duality, thus giving a nonconstructive proof of Mansfield's imprimitivity theorem. Motivated by this, we show that - for discrete groups - Mansfield's imprimitivity bimodule is in fact isomorphic to the tensor product of a Green bimodule and a coaction crossed product bimodule related to Katayama duality. A version of this identity also holds for the induced algebras arising from twisted coaction crossed products; dual versions (for actions and twisted actions) hold as well.
Date received: April 30, 1999
Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacw-53.