Duality for full crossed products of -algebras by non-amenable groups
Author:
May Nilsen
Journal:
Proc. Amer. Math. Soc. 126 (1998), 2969-2978
MSC (1991):
Primary 46L55
DOI:
https://doi.org/10.1090/S0002-9939-98-04598-5
MathSciNet review:
1469427
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a cosystem and
be a dynamical system. We examine the extent to which induction and restriction of ideals commute, generalizing some of the results of Gootman and Lazar (1989) to full crossed products by non-amenable groups. We obtain short, new proofs of Katayama and Imai-Takai duality, the faithfulness of the induced regular representation for full coactions and actions by amenable groups. We also give a short proof that the space of dual-invariant ideals in the crossed product is homeomorphic to the space of invariant ideals in the algebra, and give conditions under which the restriction mapping is open.
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Additional Information
May Nilsen
Email:
mnilsen@math.unl.edu
DOI:
https://doi.org/10.1090/S0002-9939-98-04598-5
Received by editor(s):
May 15, 1996
Received by editor(s) in revised form:
March 10, 1997
Additional Notes:
This research was supported by the Australian Research Council.
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1998
American Mathematical Society