{"paper":{"title":"Local Proof of Algebraic Characterization of Free Actions","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Paul F. Baum, Piotr M. Hajac","submitted_at":"2014-02-13T03:19:21Z","abstract_excerpt":"Let $G$ be a compact Hausdorff topological group acting on a compact Hausdorff topological space $X$. Within the $C^{*}$-algebra $C(X)$ of all continuous complex-valued functions on $X$, there is the Peter-Weyl algebra $\\mathcal{P}_G(X)$ which is the (purely algebraic) direct sum of the isotypical components for the action of $G$ on $C(X)$. We prove that the action of $G$ on $X$ is free if and only if the canonical map $\\mathcal{P}_G(X)\\otimes_{C(X/G)}\\mathcal{P}_G(X)\\to \\mathcal{P}_G(X)\\otimes\\mathcal{O}(G)$ is bijective. Here both tensor products are purely algebraic, and $\\mathcal{O}(G)$ de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3024","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"}