{"paper":{"title":"Globalizations of infinitesimal actions on supermanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Hannah Bergner","submitted_at":"2013-09-23T09:44:14Z","abstract_excerpt":"Let $\\mathcal G$ be a Lie supergroup with Lie superalgebra $\\mathfrak g$, $\\mathcal M$ a supermanifold and $\\mathrm{Vec}(\\mathcal M)$ the set of vector fields on $\\mathcal M$. Let $\\lambda:\\mathfrak g\\rightarrow \\mathrm{Vec}(\\mathcal M)$ be an infinitesimal action, i.e. a homomorphism of Lie superalgebras.\n  We show the existence of a local $\\mathcal G$-action on $\\mathcal M$ inducing the infinitesimal action $\\lambda$ and find necessary and sufficient conditions for the existence of a globalization in the sense of Palais."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5744","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"}