{"paper":{"title":"On normalizers of $C^{*}$-subalgebras in the Cuntz algebra $\\mathcal{O}_{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Tomohiro Hayashi","submitted_at":"2012-01-25T06:59:00Z","abstract_excerpt":"In this paper we investigate the normalizer $\\mathcal{N}_{\\mathcal{O}_{n}}(A)$ of a $C^{*}$-subalgebra $A\\subset \\mathcal{F}_{n}$ where $\\mathcal{F}_{n}$ is the canonical UHF-subalgebra of type $n^{\\infty}$ in the Cuntz algebra $\\mathcal{O}_{n}$. Under the assumption that the relative commutant $A'\\cap \\mathcal{F}_{n}$ is finite-dimensional, we show several facts for normalizers of $A$. In particular it is shown that the automorphism group $\\{{\\rm Ad}u|_{A}\\ \\ |\\ u\\in \\mathcal{N}_{\\mathcal{F}_{n}}(A)\\}$ has a finite index in $\\{{\\rm Ad}U|_{A}\\ \\ |\\ U\\in \\mathcal{N}_{\\mathcal{O}_{n}}(A)\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5195","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"}