Duality for full crossed products of $C^*$-algebras by non-amenable groups
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Abstract:
Let $(A, G, \delta )$ be a cosystem and $(A, G,\alpha )$ 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.References
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Additional Information
- May Nilsen
- Email: mnilsen@math.unl.edu
- 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
- © Copyright 1998 American Mathematical Society
- 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