{"paper":{"title":"Non-existence of faithful isometric action of compact quantum groups on compact, connected Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Debashish Goswami, Soumalya Joardar","submitted_at":"2013-09-05T09:48:06Z","abstract_excerpt":"Suppose that a compact quantum group $\\clq$ acts faithfully on a smooth, compact, connected manifold $M$, i.e. has a $C^*$ (co)-action $\\alpha$ on $C(M)$, such that the action $\\alpha$ is isometric in the sense of \\cite{Goswami} for some Riemannian structure on $M$.\n  We prove that $\\clq$ must be commutative as a $C^{\\ast}$ algebra i.e. $\\clq\\cong C(G)$ for some compact group $G$ acting smoothly on $M$. In particular, the quantum isometry group of $M$ (in the sense of \\cite{Goswami}) coincides with $C(ISO(M))$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1294","kind":"arxiv","version":6},"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"}