Discrete group actions and the minimal primal ideal space. (English) Zbl 0901.46057

Beckhoff, Ferdinand

Math. Scand. 80, No. 2, 289-309 (1997).

Summary: The minimal primal ideal space of a \(C^*\)-algebra \(A\) and of a crossed product \(C^*\)-algebra \(A\times_\alpha G\) is investigated. The question is, under what circumstances is it possible to tell whether Min-Primal \((A\times_\alpha G)\) is closed in the space of all proper two-sided closed ideals with the Fell topology? Positive answers are achieved in a certain class of liminal \(C^*\)-algebras with group actions that are implemented by essentially inner unitaries.

MSC:

46L55	Noncommutative dynamical systems
46L05	General theory of \(C^*\)-algebras

Keywords:

minimal primal ideal; \(C^*\)-algebra; crossed product \(C^*\)-algebra; Fell topology; essentially inner unitaries