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

DOI:
https://doi.org/10.1090/S0002-9947-2015-06406-X

Published electronically:
March 4, 2015

MathSciNet review:
3413863

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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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Additional Information

**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

Email:
alcides.buss@ufsc.br

**Siegfried Echterhoff**

Affiliation:
Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, 48149 Münster, Germany

MR Author ID:
266728

ORCID:
0000-0001-9443-6451

Email:
echters@uni-muenster.de

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