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Intermediate subalgebras of cross-product von Neumann algebras arising from weakly compact actions

  • Ionut Chifan
  • Zachary Flood
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Abstract

In this short paper, we establish the following Galois-type property for all measure-preserving, weakly compact actions $G \curvearrowright (X,μ) $ of a non-inner amenable group G on a standard probability space X: for any intermediate von Neumann subalgebra ℒ(G)⊆ 𝒩 ⊆ L∞ (X)rtimes G, there is a factor Gcurvearrowright Y of G curvearrowright X such that 𝒩= L∞(Y)rtimes G. In particular, this holds for all pmp distal actions Gcurvearrowright X, thereby answering positively an open problem from \cite{BCCMSW24} (which can also be traced back to \cite{CD20}). We also provide an example showing our result is optimal.

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Cite

BibTeXRIS
BibTeX
@misc{chifan2026intermediate,
  title = {{Intermediate subalgebras of cross-product von Neumann algebras arising from weakly compact actions}},
  author = {Ionut Chifan and Zachary Flood},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33320},
  eprint = {2610.33320},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33320},
}
RIS
TY  - UNPB
TI  - Intermediate subalgebras of cross-product von Neumann algebras arising from weakly compact actions
AU  - Ionut Chifan
AU  - Zachary Flood
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.33320
UR  - https://arxiv.org/abs/2610.33320
AB  - In this short paper, we establish the following Galois-type property for all measure-preserving, weakly compact actions $G \curvearrowright (X,μ) $ of a non-inner amenable group G on a standard probability space X: for any intermediate von Neumann subalgebra ℒ(G)⊆ 𝒩 ⊆ L^∞ (X)rtimes G, there is a factor Gcurvearrowright Y of G curvearrowright X such that 𝒩= L^∞(Y)rtimes G. In particular, this holds for all pmp distal actions Gcurvearrowright X, thereby answering positively an open problem from \cite{BCCMSW24} (which can also be traced back to \cite{CD20}). We also provide an example showing our result is optimal.
ER  -