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Transactions of the American Mathematical Society

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Weakly proper group actions, Mansfield’s Imprimitivity and twisted Landstad duality

Authors: Alcides Buss and Siegfried Echterhoff
Journal: Trans. Amer. Math. Soc. 368 (2016), 249-280
MSC (2010): Primary 46L55, 22D35
Published electronically: March 4, 2015
MathSciNet review: 3413863
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Abstract: Using the theory of weakly proper actions of locally compact groups recently developed by the authors, we give a unified proof of both reduced and maximal versions of Mansfield’s Imprimitivity Theorem and obtain a general version of Landstad’s Duality Theorem for twisted group coactions. As one application, we obtain the stabilization trick for arbitrary twisted coactions, showing that every twisted coaction is Morita equivalent to an inflated coaction.

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Alcides Buss
Affiliation: Departamento de Matemática, Universidade Federal de Santa Catarina, 88.040-900 Florianópolis-SC, Brazil
MR Author ID: 827256
ORCID: 0000-0001-6796-9818

Siegfried Echterhoff
Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, 48149 Münster, Germany
MR Author ID: 266728
ORCID: 0000-0001-9443-6451

Keywords: Weakly proper group action, generalized fixed-point algebra, Mansfield Imprimitivity Theorem, exotic crossed product, twisted group coactions, Landstad Duality
Received by editor(s): October 30, 2013
Published electronically: March 4, 2015
Additional Notes: This research was supported by Deutsche Forschungsgemeinschaft (SFB 878, Groups, Geometry & Actions) and by CNPq (Ciências sem Fronteira) – Brazil.
Article copyright: © Copyright 2015 American Mathematical Society