Mansfield’s imprimitivity theorem for full crossed products
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- by S. Kaliszewski and John Quigg PDF
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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 $A\times _\delta G\times _{\widehat \delta |}N$ 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 “${}\times G\times N$” 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 $G$.References
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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
- Received by editor(s): December 12, 2003
- Published electronically: November 4, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 2021-2042
- MSC (2000): Primary 46L55
- DOI: https://doi.org/10.1090/S0002-9947-04-03683-9
- MathSciNet review: 2115089