Jaime–Willett question on complexity rank of AT algebras
Is it true that every separable unital algebra of real rank zero satisfies ? In particular, for every irrational rotation algebra with irrational , is ?
References
Primary source
Additional references
- Complexity Rank of AT Algebras of Real Rank Zero — arXiv — Qingnan An, Kang Li, Zhichao Liu
Progress summary
A new unrefereed paper claims the question has a positive answer for every real-rank-zero AT algebra, but that claim has not been independently checked.
The 2023 paper Complexity rank for -algebras posed the question for irrational rotation algebras and, more generally, separable real-rank-zero -algebras that are not . It conjectured complexity rank one in these cases.
Known results
- Every unital UCT Kirchberg algebra has complexity rank one or two; rank one occurs exactly when its -group is torsion-free (2023).
New class-wide rank-one claim
The preprint Complexity Rank of AT Algebras of Real Rank Zero, by Qingnan An, Kang Li, and Zhichao Liu, claims a uniform rank-one bound for real-rank-zero -algebras and identifies irrational rotation algebras as rank one. The claim is unrefereed and has no independent mathematical verification in the retrieved sources.
Current status (as of October 2026): The rank-one conjecture for real-rank-zero -algebras is claimed to be settled by an unverified preprint; the earlier Kirchberg-algebra results remain established partial results.
Solutions 0
No solutions have been posted yet.