{"paper":{"title":"A class of groups for which every action is W*-superrigid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Cyril Houdayer, Sorin Popa, Stefaan Vaes","submitted_at":"2010-10-25T10:16:56Z","abstract_excerpt":"We prove the uniqueness of the group measure space Cartan subalgebra in crossed products A \\rtimes \\Gamma covering certain cases where \\Gamma is an amalgamated free product over a non-amenable subgroup. In combination with Kida's work we deduce that if \\Sigma < SL(3,\\Z) denotes the subgroup of matrices g with g_31 = g_32 = 0, then any free ergodic probability measure preserving action of \\Gamma = SL(3,\\Z) *_\\Sigma SL(3,\\Z) is stably W*-superrigid. In the second part we settle a technical issue about the unitary conjugacy of group measure space Cartan subalgebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5077","kind":"arxiv","version":3},"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"}