Equivariance implies admissibility for groupoid Busby homomorphisms

About 2 years old · traced to

Let GG be a second countable groupoid, (A,α)(A,\alpha) and (I,γ)(I,\gamma) be separable, GG-C∗C^*-algebras, and let μ ⁣:A→Q(I)\mu\colon A\to\mathcal{Q}(I) be a ∗*-homomorphism.

Equivariance-implies-admissibility conjecture. If μ\mu is GG-equivariant, then μ\mu is GG-admissible.

For locally compact, Hausdorff, second countable groups, the corresponding equivalence between GG-admissibility and GG-equivariance is established in the preceding corollary. The conjecture asks whether the converse implication remains valid for general second countable groupoids.

References

Primary source

Suvrajit Bhattacharjee and Marzieh Forough, “Quasi-invariant lifts of completely positive maps for groupoid actions”, arXiv:2405.07859 (2026).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.