Dynamical characterization of simplicity

Give a dynamical, and possibly group-theoretic, characterization of simplicity for the reduced crossed product of a dynamical system.

Background

For amenable actions, simplicity is characterized by minimality and topological freeness. The survey states that no corresponding general characterization is known without amenability and relates the problem to a question involving C*-simplicity of the group and open stabilizers.

References

Problem 6.2.1. Give a dynamical (and possibly also group-theoretic) characteri- zation of simplicity for the crossed product of a dynamical system. Some work exists [1], but Ozawa’s question remains unanswered: is G ↷ X C*-simple if and only if G ↷ X is minimal and every open stabilizer is C*-simple?

— Classifiability of crossed products  (2610.06586 - Gardella, 5 Oct 2026) in Problem 6.2.1, Section 6.2, p. 48