{"paper":{"title":"Stable rank for crossed products by actions of finite groups on C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Hiroyuki Osaka","submitted_at":"2017-08-08T22:17:24Z","abstract_excerpt":"Let $G$ be a finite group, $A$ a unital separable finite simple nuclear C*-algebra, and $\\alpha$ an action of $G$ on $A$. Assume that $A$ absorbs the Jiang-Su algebra $\\mathcal{Z}$, the extremal boundary of the trace space of $A$ is compact and finite dimensional and that $\\alpha$ fixes any tracial state of $A$. Then tsr$(A \\rtimes_\\alpha G) = 1$. In particular, when $A$ has a unique tracial state, we conclude it without above conditons on a tracial state space of $A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02665","kind":"arxiv","version":1},"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"}