Trace-space computation for an allosteric action

Explicitly compute the trace space of the crossed product associated to one of Joseph’s allosteric actions G ↷ X.

Background

Allosteric actions are minimal and topologically free but not essentially free. The survey explains that the trace theory of their crossed products is not yet understood in a comparable systematic way, making an explicit computation for Joseph’s examples a concrete unresolved problem.

References

Problem 6.1.1. For one of the allosteric actions G ↷ X constructed by Joseph, explicitly compute the trace space of C(X) ⋊ G.

— Classifiability of crossed products  (2610.06586 - Gardella, 5 Oct 2026) in Problem 6.1.1, Section 6.1, p. 47

Problem 6.1.2. Construct more examples of allosteric actions of amenable groups.

— Classifiability of crossed products  (2610.06586 - Gardella, 5 Oct 2026) in Problem 6.1.2, Section 6.1, p. 47