Robert–Tikuisis regularity equivalence for nonsimple C*-algebras
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For separable nuclear complex C*-algebras with no nonzero elementary ideal subquotients, are finite nuclear dimension, Jiang–Su stability and nuclear dimension at most one equivalent?
Why it matters and what counts as progress
Why it matters: The nonsimple equivalence would extend regularity results beyond simple unital algebras while retaining the elementary-subquotient obstruction.
What counts as progress: A proof of the equivalence in this precise class, or a counterexample; the separate estimate dim_nuc(A₀⊗Z)≤1 has its own broader scope.
How the problem developed
- 2015 · Partial result [1]
Yoshimichi Sato, Stuart White and Wilhelm Winter Proved finite nuclear dimension for simple separable unital monotracial nuclear C*-algebras absorbing the Jiang–Su algebra, a simple-algebra precursor to later regularity equivalences.
- 23 Sept 2026 · Proof claim [2]
OpenAI A manuscript claims equivalence of finite nuclear dimension, Jiang–Su stability and nuclear dimension at most one for separable nuclear complex C*-algebras without nonzero elementary ideal subquotients.
AI contribution
Nuclear dimension and Jiang–Su stability without elementary subquotients
For separable nuclear complex C*-algebras with no nonzero elementary ideal subquotients, the manuscript claims finite nuclear dimension, Jiang–Su stability and nuclear dimension at most one are equivalent. It separately claims dim_nuc(A₀⊗Z)≤1 for every separable nuclear A₀.
Sources
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Publication dates and editorial changes.
OpenAI reports nonsimple Robert–Tikuisis regularity equivalence