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This article studies the superizations of M_0, i.e. its extensions to a homogeneous supermanifold M=G/H whose sheaf of superfunctions is isomorphic to Lambda(S^*(M_0)). Here G is the Lie supergroup associated with a certain extension of the Lie algebra of symmetry g_0 to an algebra of supersymmetry g=g_0+g_1=g_0+S via the Kostant-Koszul construction. Each algebra of supersymmetry naturally"},"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":"0905.3832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-24T12:25:33Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"7d8bf27d80294b88bd1646500b4ed81e4c99339b7a5f5c6bf6b975853a5a8c62","abstract_canon_sha256":"e2fc784d9c519e64464978a0837083e8119816aff4f408d121f37c016cbc60cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:24.568278Z","signature_b64":"NrJ9XfbiAr4YPzBeTPGkLJXRXfnJfO4VPo+poYYq+eL2vdV2hklNctksexjI6qxpN6DoESn98AAnY1z4UjBVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b82572621328c7da1cfb440726f4f0e17096264a612c15122285b93746b3eea1","last_reissued_at":"2026-05-18T03:19:24.567552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:24.567552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Superization of Homogeneous Spin Manifolds and Geometry of Homogeneous Supermanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Andrea Santi","submitted_at":"2009-05-24T12:25:33Z","abstract_excerpt":"Let M_0=G_0/H be a (pseudo)-Riemannian homogeneous spin manifold, with reductive decomposition g_0=h+m and let S(M_0) be the spin bundle defined by the spin representation Ad:H->\\GL_R(S) of the stabilizer H. 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