2408.10047
Cuntz–Pimsner algebras of partial automorphisms twisted by vector bundles I: Fixed point algebra, simplicity and the tracial state space
Aaron Kettner
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s main theorem (continuity of the gauge core as a C0(X)-algebra and the precise fiber descriptions) is correct and rigorously proved via the B[0,n]-core, pushouts, and fiberwise analysis. The candidate solution reaches the same conclusions with a broadly similar structural route (Fock core, inductive limits, fiber computations), but contains one substantive misstatement in Step 1 (claiming φ(f)∈K(E) for all f), which conflicts with the paper’s Lemma 3.12. Once that point is corrected to φ−1(K(E))=C0(V), the remainder of the model’s proof aligns with the paper’s results and is essentially correct.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript gives a careful and correct analysis of the fixed-point algebra in the twisted partial automorphism setting, proving continuity and computing fibers. The approach via graded cores, pushouts, and fiberwise limits is solid and broadly useful. Exposition is generally clear, though notational overload and the abundance of structures could be streamlined. With small clarifications, this will be a nice contribution for specialists.