{"paper":{"title":"Amalgamated Free Product Rigidity for Group von Neumann Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Adrian Ioana, Ionut Chifan","submitted_at":"2017-05-20T19:54:42Z","abstract_excerpt":"We provide a fairly large family of amalgamated free product groups $\\Gamma=\\Gamma_1\\ast_{\\Sigma}\\Gamma_2$ whose amalgam structure can be completely recognized from their von Neumann algebras. Specifically, assume that $\\Gamma_i$ is a product of two icc non-amenable bi-exact (e.g., hyperbolic) groups, and $\\Sigma$ is icc amenable and has trivial one-sided commensurator in $\\Gamma_i$, for every $i\\in\\{1,2\\}$. Then $\\Gamma$ satisfies the following rigidity property: any group $\\La$ such that $L(\\La)$ is isomorphic to $L(\\G)$ admits an amalgamated free product decomposition $\\La=\\La_1\\ast_\\Delta "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07350","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":""},"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"}