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)|
|Number of pages||10|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - Dec 1 1998|
ASJC Scopus subject areas
- Applied Mathematics