{"paper":{"title":"A retract theorem for nilpotent Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Carine Molitor-Braun, Jean Ludwig, Ying-Fen Lin","submitted_at":"2016-10-05T17:21:51Z","abstract_excerpt":"Let $G= \\exp(\\g)$ be a connected, simply connected nilpotent Lie group. We show that for every $G$-invariant smooth sub-manifold $M$ of $g^*$, there exists an open relatively compact subset $\\mathcal{M}$ of $M$ such that for any smooth adapted field of operators $(F(l))_{l\\in M}$ supported in $G\\cdot \\mathcal{M}$ there exists a Schwartz function $f$ on $G$ such that $\\pi_l(f)= \\op_{F(l)}$ for all $l\\in M$. This retract theorem can then be used to show that for every Lie group $\\G$ of automorphisms of $G$ containing the inner automorphisms of $G$ with locally closed $\\G$-orbits in $\\g^*$, the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01535","kind":"arxiv","version":1},"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"}