CROSSED PRODUCT SPLITTING OF INTERMEDIATE OPERATOR ALGEBRAS VIA 2-COCYCLES

Yuhei Suzuki

correctmedium confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The candidate solution reproduces the paper’s O2-stabilized splitting of intermediate algebras under C*-irreducibility, central Γ-freeness, and AP. Its steps (Fourier coefficient spaces, central-freeness averaging, dichotomy yielding unitaries, subgroup support, and the AP-based coefficient test to identify a twisted crossed product) mirror Lemmas 3.1, 3.3 and the coefficient-characterization (Lemma 2.2 and its cocycle generalization Lemma 4.2) used in the proof of Theorem A and Theorem 4.4 of the paper. No essential gaps or contradictory claims were found; differences are expository and not mathematical.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper gives a robust and conceptually streamlined O2-stabilized splitting theorem for intermediate inclusions under central Γ-freeness and AP, and convincingly establishes the necessity of O2 and the persistence of cocycles via examples. The proof is correct and well-organized. Minor clarifications (explicit early statement of the coefficient test; brief schematic of the averaging argument; a roadmap for the cocycle/non-unital extension) would further enhance readability.