{"paper":{"title":"Similarity degree of a class of C$^*$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Junhao Shen, Wenhua Qian","submitted_at":"2014-07-05T00:18:59Z","abstract_excerpt":"Suppose that $\\mathcal M$ is a countably decomposable type II$_1$ von Neumann algebra and $\\mathcal A$ is a separable, non-nuclear, unital C$^*$-algebra. We show that, if $\\mathcal M$ has Property $\\Gamma$, then the similarity degree of $\\mathcal M$ is less than or equal to $5$. If $\\mathcal A$ has Property c$^*$-$\\Gamma$, then the similarity degree of $\\mathcal A$ is equal to $3$. In particular, the similarity degree of a $\\mathcal Z$-stable, separable, non-nuclear, unital C$^*$-algebra is equal to $3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1348","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"}