{"paper":{"title":"The pure extension property for discrete crossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Vrej Zarikian","submitted_at":"2017-08-14T01:54:21Z","abstract_excerpt":"Let $G$ be a discrete group acting on a unital $C^*$-algebra $\\mathcal{A}$ by $*$-automorphisms. In this note, we show that the inclusion $\\mathcal{A} \\subseteq \\mathcal{A} \\rtimes_r G$ has the pure extension property (so that every pure state on $\\mathcal{A}$ extends uniquely to a pure state on $\\mathcal{A} \\rtimes_r G$) if and only if $G$ acts freely on $\\mathcal{\\widehat{A}}$, the spectrum of $\\mathcal{A}$. The same characterization holds for the inclusion $\\mathcal{A} \\subseteq \\mathcal{A} \\rtimes G$. This generalizes what was already known for $\\mathcal{A}$ abelian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03987","kind":"arxiv","version":2},"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"}