Relative invariant subalgebra rigidity for Thompson's group $F$
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917552540614656 |
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| author | Amrutam, Tattwamasi Dudko, Artem |
| author_facet | Amrutam, Tattwamasi Dudko, Artem |
| contents | We prove that Thompson's group $F$ satisfies the relative invariant subalgebra rigidity property with respect to its commutator subgroup: every von Neumann subalgebra of $L(F)$ that is invariant under conjugation by $[F,F]$ is of the form $L(N)$ for some normal subgroup $N \trianglelefteq F$. Along the way, we establish a general factoriality criterion for invariant subalgebras whose hypotheses are met whenever the ambient group is i.c.c., simple, and every faithful ergodic measure-preserving action of it on a probability space is essentially free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01268 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Relative invariant subalgebra rigidity for Thompson's group $F$ Amrutam, Tattwamasi Dudko, Artem Operator Algebras Dynamical Systems Functional Analysis General Topology We prove that Thompson's group $F$ satisfies the relative invariant subalgebra rigidity property with respect to its commutator subgroup: every von Neumann subalgebra of $L(F)$ that is invariant under conjugation by $[F,F]$ is of the form $L(N)$ for some normal subgroup $N \trianglelefteq F$. Along the way, we establish a general factoriality criterion for invariant subalgebras whose hypotheses are met whenever the ambient group is i.c.c., simple, and every faithful ergodic measure-preserving action of it on a probability space is essentially free. |
| title | Relative invariant subalgebra rigidity for Thompson's group $F$ |
| topic | Operator Algebras Dynamical Systems Functional Analysis General Topology |
| url | https://arxiv.org/abs/2606.01268 |