Renault's essential freeness conjecture for reduced crossed products

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Let (A,G)(A,G) be a C*-dynamical system with GG discrete. The action of GG on the spectrum A^\widehat{A} is called essentially free if, for every closed invariant subset Y⊆A^Y\subseteq\widehat{A}, the points in YY with trivial isotropy are dense in YY. Renault's essential freeness conjecture. If the action of GG on A^\widehat{A} is essentially free, then AA separates the ideals in the reduced crossed product A⋊rGA\rtimes_r G. The claim would characterize essential freeness as sufficient for ideal separation in reduced crossed products, extending the role of topological freeness beyond the amenable or abelian settings. The supplied text attributes the claim to Renault and gives no resolution.

References

Primary source

Adam Sierakowski, “The ideal structure of reduced crossed products”, arXiv:0804.3772 (2009).

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