{"paper":{"title":"Classification of type III Bernoulli crossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Peter Verraedt, Stefaan Vaes","submitted_at":"2014-08-27T13:57:01Z","abstract_excerpt":"Crossed products with noncommutative Bernoulli actions were introduced by Connes as the first examples of full factors of type III. This article provides a complete classification of the factors $(P,\\phi)^{\\mathbb{F}_n} \\rtimes \\mathbb{F}_n$, where $\\mathbb{F}_n$ is the free group and P is an amenable factor with an almost periodic state $\\phi$. We show that these factors are completely classified by the rank n of the free group $\\mathbb{F}_n$ and Connes's Sd-invariant. We prove similar results for free product groups, as well as for classes of generalized Bernoulli actions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6414","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"}