{"paper":{"title":"A Unique Decomposition Result for HT Factors with Torsion Free Core","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Sorin Popa","submitted_at":"2004-01-14T05:28:10Z","abstract_excerpt":"We prove that II$_1$ factors $M$ have a unique (up to unitary conjugacy) cross-product type decomposition around ``core subfactors'' $N \\subset M$ satisfying the property HT and a certain ``torsion freeness'' condition. In particular, this shows that isomorphism of factors of the form $L_\\alpha(\\Bbb Z^2) \\rtimes \\Gamma$, for torsion free, non-amenable subgroups $\\Gamma\\subset SL(2, \\Bbb Z)$ and $\\alpha = e^{2\\pi i t}$, $t \\not\\in \\Bbb Q$, implies isomorphism of the corresponding groups $\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401138","kind":"arxiv","version":5},"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/math/0401138/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"}