{"paper":{"title":"Non-existence of genuine (compact) quantum symmetries of compact, connected smooth manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Debashish Goswami","submitted_at":"2018-05-14T05:00:37Z","abstract_excerpt":"Suppose that a compact quantum group ${\\mathcal Q}$ acts faithfully on a smooth, compact, connected manifold $M$, i.e. has a $C^{\\ast}$ (co)-action $\\alpha$ on $C(M)$, such that $\\alpha(C^\\infty(M)) \\subseteq C^\\infty(M, {\\mathcal Q})$ and the linear span of $\\alpha(C^\\infty(M))(1 \\otimes {\\mathcal Q})$ is dense in $C^\\infty(M, {\\mathcal Q})$ with respect to the Frechet topology.\n  It was conjectured by the author quite a few years ago that ${\\mathcal Q}$ must be commutative as a $C^{\\ast}$ algebra i.e. ${\\mathcal Q} \\cong C(G)$ for some compact group $G$ acting smoothly on $M$. The goal of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05765","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"}