2403.20299
Every locally compact group is the outer automorphism group of a II1 factor
Stefaan Vaes
correctmedium confidence
- Category
- math.DS
- Journal tier
- Top Field-Leading
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem A proves that every lcsc group G is Out(M) for some full II1 factor with separable predual, by reducing to centralizer groups via Poisson suspensions and the Maharam extension (Theorem C, with key Lemmas 3.1 and 3.2), and then invoking Deprez [Theorem E] and Popa–Vaes [Prop. 8.5] to realize any such centralizer group as Out(M) . The candidate solution follows this same two-step strategy at a high level and is aligned with the paper’s approach, differing only in omitted technical details (e.g., explicit ergodicity and countable reduction arguments).
Referee report (LaTeX)
\textbf{Recommendation:} no revision
\textbf{Journal Tier:} top field-leading
\textbf{Justification:}
The paper resolves a broad realization problem by showing that every lcsc group occurs as the outer automorphism group of a full II1 factor. The strategy is elegant and modular: a precise centralizer-group framework, strengthened by Poisson suspension and Maharam extension techniques, feeds into established W*-rigidity realization theorems. The exposition is succinct yet complete on the key technical points and should be accessible to specialists in operator algebras and ergodic theory.