{"paper":{"title":"The Automorphism group of a simple $\\mathcal{Z}$-stable $C^{*}$-algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Efren Ruiz, Ping Wong Ng","submitted_at":"2010-03-11T19:52:40Z","abstract_excerpt":"We study the automorphism group of a unital, simple, $\\mathcal{Z}$-stable $C^{*}$-algebra. In this paper, we generalize the results by the authors in \\cite{pr_auto} to $\\mathcal{Z}$-stable $C^{*}$-algebras $\\mathfrak{A}$ such that $\\mathfrak{A} \\otimes \\mathfrak{B}$ is a separable, nuclear, simple, tracially AI algebras satisfying the Universal Coefficient Theorem (UCT) of Rosenberg and Schochet \\cite{uct}. By the results of Lin in \\cite{hl_asyunit} and Winter in \\cite{ww_localelliott}, $C^{\\ast}$-algebras that satisfies the above condition are classified via $K$-theory and traces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2404","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"}