{"paper":{"title":"Solidity of type III Bernoulli crossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Amine Marrakchi","submitted_at":"2016-01-14T17:04:24Z","abstract_excerpt":"We generalize a theorem of Chifan and Ioana by proving that for any, possibly type III, amenable von Neumann algebra $A_0$, any faithful normal state $\\varphi_0$ and any discrete group $\\Gamma$, the associated Bernoulli crossed product von Neumann algebra $M=(A_0,\\varphi_0)^{\\mathbin{\\bar{\\otimes}}\\Gamma}\\rtimes \\Gamma$ is solid relatively to $\\mathcal{L}(\\Gamma)$. In particular, if $\\mathcal{L}(\\Gamma)$ is solid then $M$ is solid and if $\\Gamma$ is non-amenable and $A_0 \\neq \\mathbb{C}$ then $M$ is a full prime factor. This gives many new examples of solid or prime type $\\mathrm{III}$ factors"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03666","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"}