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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Mansfield's imprimitivity theorem for full crossed products


Authors: S. Kaliszewski and John Quigg
Journal: Trans. Amer. Math. Soc. 357 (2005), 2021-2042
MSC (2000): Primary 46L55
Published electronically: November 4, 2004
MathSciNet review: 2115089
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Abstract: For any maximal coaction $(A,G,\delta)$ and any closed normal subgroup $N$ of $G$, 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 $G$. 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 $G$ and whose morphisms are isomorphism classes of right-Hilbert bimodule coactions of $G$.


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Additional Information

S. Kaliszewski
Affiliation: Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287
Email: kaliszewski@asu.edu

John Quigg
Affiliation: Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287
Email: quigg@math.asu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03683-9
PII: S 0002-9947(04)03683-9
Keywords: $C^*$-algebra, locally compact group, coaction, right-Hilbert bimodule, duality, naturality
Received by editor(s): December 12, 2003
Published electronically: November 4, 2004
Article copyright: © Copyright 2004 American Mathematical Society