Mansfieldβs 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
DOI:
https://doi.org/10.1090/S0002-9947-04-03683-9
Published electronically:
November 4, 2004
MathSciNet review:
2115089
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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 $A\times _\delta G\times _{\widehat \delta |}N$ and $A\times _{\delta |}G/N$, together with $\operatorname {Inf}\widehat {\widehat \delta |}-\delta ^{\text {dec}}$ 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 β${}\times G\times N$β and β${}\times G/N$β, 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
MR Author ID:
341615
Email:
kaliszewski@asu.edu
John Quigg
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287
MR Author ID:
222703
Email:
quigg@math.asu.edu
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