Imprimitivity theorems for weakly proper actions of locally compact groups
Abstract
In a recent paper the authors introduced universal and exotic generalized fixed-point algebras for weakly proper group actions on C*-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 GxH. In addition, we study functorial properties of generalized fixed-point algebras for equivariant categories of C*-algebras based on correspondences.
Keywords
Cite
@article{arxiv.1305.5100,
title = {Imprimitivity theorems for weakly proper actions of locally compact groups},
author = {Alcides Buss and Siegfried Echterhoff},
journal= {arXiv preprint arXiv:1305.5100},
year = {2015}
}
Comments
The article has been completely revised. In the second version, the main part of the paper on imprimitivity theorems has been re-written and generalized to exotic crossed products. The third version essencially only contains minor changes and improvements in the text. The article has now 43 pages. Version accepted for publications in Erg. Theory and Dyn. Systems