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

Nilsen, May

doi:10.1090/S0002-9939-98-04598-5

Duality for full crossed products of $C^{\displaystyle *}\!$ -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: 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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