Duality for full crossed products of c*-algebras by non-amenable groups

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Abstract

Let (A, G, δ) be a cosystem and (.A, G, α) 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.

Original languageEnglish (US)
Pages (from-to)2969-2978
Number of pages10
JournalProceedings of the American Mathematical Society
Volume126
Issue number10
StatePublished - Dec 1 1998
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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