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Mansfield's imprimitivity theorem for full crossed products

Authors:	S Kaliszewski John Quigg

Institution:	Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287 ; Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287

Abstract:	For any maximal coaction $(A,G,\delta)$ and any closed normal subgroup of , there exists an imprimitivity bimodule $Y_{G/N}^G(A)$ between the full crossed product $A\times_\delta G\times_{\widehat\delta\vert}N$ and $A\times_{\delta\vert}G/N$ , together with $\operatorname{Inf}\widehat{\widehat\delta\vert}-\delta^{\text{dec}}$ compatible coaction $\delta_Y$ of . The assignment $(A,\delta)\mapsto (Y_{G/N}^G(A),\delta_Y)$ implements a natural equivalence between the crossed-product functors `` ${}\times G\times N$ ' and `` ${}\times G/N$ ', in the category whose objects are maximal coactions of and whose morphisms are isomorphism classes of right-Hilbert bimodule coactions of .

Keywords:	$C^*$-algebra locally compact group coaction right-Hilbert bimodule duality naturality

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