{"paper":{"title":"An example of an infinite amenable group with the ISR property","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Xiaoyan Zhou, Yongle Jiang","submitted_at":"2023-12-13T11:16:41Z","abstract_excerpt":"Let $G$ be $S_{\\mathbb{N}}$, the finitary permutation (i.e. permutations with finite support) group on positive integers $\\mathbb{N}$. We prove that $G$ has the invariant von Neumann subalgebras rigidity (ISR, for short) property as introduced in Amrutam-Jiang's work. More precisely, every $G$-invariant von Neumann subalgebra $P\\subseteq L(G)$ is of the form $L(H)$ for some normal sugbroup $H\\lhd G$ and in this case, $H=\\{e\\}, A_{\\mathbb{N}}$ or $G$, where $A_{\\mathbb{N}}$ denotes the finitary alternating group on $\\mathbb{N}$, i.e. the subgroup of all even permutations in $S_{\\mathbb{N}}$. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.08061","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.08061/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}