{"paper":{"title":"Hochschild cohomology of type II$_1$ von Neumann algebras with Property $\\Gamma$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Junhao Shen, Wenhua Qian","submitted_at":"2014-07-02T18:01:30Z","abstract_excerpt":"In this paper, Property $\\Gamma$ for a type II$_{1}$ von Neumann algebra is introduced as a generalization of Murray and von Neumann's Property $\\Gamma$ for a type II$_{1}$ factor. The main result of this paper is that if a type II$_{1}$ von Neumann algebra $\\mathcal{M}$ with separable predual has Property $\\Gamma$, then the continuous Hochschild cohomology group $H^{k}(\\mathcal{M}, \\mathcal{M})$ vanishes for every $k \\geq 2$. This gives a generalization of an earlier result due to E. Christensen, F. Pop, A.M. Sinclair and R.R. Smith."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0664","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"}