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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.5744","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-23T09:44:14Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"4193cf6a3731007eaa7246164492ca97d5a1dabb3666dceea8d470cb9830a00e","abstract_canon_sha256":"a33739a2ed6b9c090b9cffc39686e77300d7be668987b6cd28876deeb964a69f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:34.313420Z","signature_b64":"wBU8A2u28SJOU8hVNFJc2XmrdsyMAGKTkEjr1mBHwpKnE7KerAxDz1enbgZzdFB6Val9Lhmn/PiuiXz5MkYoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35e626889927c75163de2e46f4a49708d3bdcf9c8256ac9bcbd66be8bbe1e6e8","last_reissued_at":"2026-05-18T03:12:34.312683Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:34.312683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathcal M$. 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