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Imprimitivity theorems for weakly proper actions of locally compact groups

Published online by Cambridge University Press:  04 August 2014

ALCIDES BUSS  and
SIEGFRIED ECHTERHOFF
ALCIDES BUSS
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, 88.040-900 Florianópolis-SC, Brazil email [email protected]
SIEGFRIED ECHTERHOFF
Affiliation:
Mathematisches Institut, University of Münster, Einsteinstr. 62, 48149 Münster, Germany email [email protected]
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Abstract

In a recent paper the authors introduced universal and exotic generalized fixed-point algebras for weakly proper group actions on $C^{\ast }$-algebras. Here we extend the notion of weakly proper actions to actions on Hilbert modules. As a result we obtain several imprimitivity theorems establishing important Morita equivalences between universal, reduced, or exotic crossed products and appropriate universal, reduced, or exotic fixed-point algebras, respectively. In particular, we obtain an exotic version of Green’s imprimitivity theorem and a very general version of the symmetric imprimitivity theorem by weakly proper actions of product groups $G\times H$. In addition, we study functorial properties of generalized fixed-point algebras for equivariant categories of $C^{\ast }$-algebras based on correspondences.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 8 , December 2015 , pp. 2412 - 2457
Copyright
© Cambridge University Press, 2014 

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