{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DDVU64VBXLMCFZLSSRPLUUUGIK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"14cd6e32a420c231b63f325438e95e20bb7e7f07877730a1573da53252c81d34","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-03T15:16:01Z","title_canon_sha256":"3a716b57cc56b71f152735968e1a3459951d6a1c2b8c2e9b499a966a3857942c"},"schema_version":"1.0","source":{"id":"1109.0626","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0626","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0626v7","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0626","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"pith_short_12","alias_value":"DDVU64VBXLMC","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DDVU64VBXLMCFZLS","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DDVU64VB","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:8460ce1bbb3183137a6a44e19a0747d372d69cf6f2c142dcde241c66effe45a8","target":"graph","created_at":"2026-05-18T01:27:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"I present a construction of connected affine algebraic supergroups G_V associated with simple Lie superalgebras g of Cartan type and with g-modules V. Conversely, I prove that every connected affine algebraic supergroup whose tangent Lie superalgebra is of Cartan type is necessarily isomorphic to one of the supergroups G_V that I introduced. In particular, the supergroup constructed in this way associated with g := W(n) and its standard representation is described somewhat more in detail.\n  In addition, *** an \"Erratum\" is added here *** after the main text to fix a mistake which was kindly po","authors_text":"Fabio Gavarini","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-03T15:16:01Z","title":"Algebraic supergroups of Cartan type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0626","kind":"arxiv","version":7},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:001511f96806ca0f9694f4388811dee83b5208e1ef4fca0d5c4e457515eacff5","target":"record","created_at":"2026-05-18T01:27:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"14cd6e32a420c231b63f325438e95e20bb7e7f07877730a1573da53252c81d34","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-03T15:16:01Z","title_canon_sha256":"3a716b57cc56b71f152735968e1a3459951d6a1c2b8c2e9b499a966a3857942c"},"schema_version":"1.0","source":{"id":"1109.0626","kind":"arxiv","version":7}},"canonical_sha256":"18eb4f72a1bad822e572945eba528642a516bf5d890c6e6e15bda4d97d2a929a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18eb4f72a1bad822e572945eba528642a516bf5d890c6e6e15bda4d97d2a929a","first_computed_at":"2026-05-18T01:27:38.824273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:38.824273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y8eWpJxt8VRzeMas/puvvFxUO6dPIaZ5GSeUMEm84xxdTD0ayVC4lcRZEDPt9vNQ5n04xm97FhF9aoRyh/yGCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:38.824980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0626","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:001511f96806ca0f9694f4388811dee83b5208e1ef4fca0d5c4e457515eacff5","sha256:8460ce1bbb3183137a6a44e19a0747d372d69cf6f2c142dcde241c66effe45a8"],"state_sha256":"26ae1064983d2450868810bd5244d872e130771c9c8b45d0a2b8994a5260b762"}