{"paper":{"title":"Nuclear dimension for an inclusion of unital C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Hiroyuki Osaka, Tamotsu Teruya","submitted_at":"2011-11-08T05:59:37Z","abstract_excerpt":"Let $P \\subset A$ be an inclusion of separable unital C*-algebras with finite Watatani index. Suppose that $E \\colon A \\rightarrow P$ has the Rokhlin property, that is, there is a projection $e \\in A' \\cap A^\\infty$ such that $E^\\infty(e) = ({\\rm Index}E)^{-1}1$. We show that if $A$ has nuclear dimension $n$, then $P$ has nuclear dimension less than or equal to $n$. In particular, if an action $\\alpha$ of a finite group $G$ on $A$ has the Rokhlin property, then the nuclear dimension of the crossed product algebra $A \\rtimes_\\alpha G$ is less than or equal to that of $A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1808","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"}