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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Duality for full crossed products of $C^*$-algebras by non-amenable groups
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by May Nilsen PDF
Proc. Amer. Math. Soc. 126 (1998), 2969-2978 Request permission

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.
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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