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 language | English (US) |
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Pages (from-to) | 2969-2978 |
Number of pages | 10 |
Journal | Proceedings of the American Mathematical Society |
Volume | 126 |
Issue number | 10 |
DOIs | |
State | Published - 1998 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics