{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:EHUCZ6CQMPUT3CVN5EDVEKKMFE","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":"96c870cba71f0a2b334584e2205b80c8eb01617d0c485335eaddf6207614fa98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"1998-03-23T13:29:16Z","title_canon_sha256":"9282a0f5bfb51d9b6e8dcc2d2333b549674da6630d33242e5071c1026839612a"},"schema_version":"1.0","source":{"id":"math/9803104","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9803104","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/9803104v2","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9803104","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"pith_short_12","alias_value":"EHUCZ6CQMPUT","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"EHUCZ6CQMPUT3CVN","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"EHUCZ6CQ","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:0aa7c1540440985c42ec1c9d1e69c58a95e6b3158d44cfa8a6516901c05857ca","target":"graph","created_at":"2026-05-18T00:43:03Z","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":"Let $ \\mathfrak{g} $ be a quasitriangular Lie bialgebra over a field $ K $ of characteristic zero, and let $ \\mathfrak{g}^* $ be its dual Lie bialgebra. We prove that the formal Poisson group $ K\\big[\\big[\\mathfrak{g}^*\\big]\\big] $ is a braided Hopf algebra, thus generalizing a result due to Reshetikhin (in the case $ \\, \\mathfrak{g} = \\mathfrak{sl}(2,K) \\, $). The proof is via quantum groups, using the existence of a quasitriangular quantization of $ \\mathfrak{g}^* $, as well as the fact that this one provides also a quantization of $ K\\big[\\big[\\mathfrak{g}^*\\big]\\big] \\, $.","authors_text":"Fabio Gavarini, Gilles Halbout","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"1998-03-23T13:29:16Z","title":"Tressages des groupe de Poisson formels \\`a dual quasitriangulaire"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9803104","kind":"arxiv","version":2},"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:c7da7c3753ddd55f9eee11f41763e1cbf1cac798d31cb726b58589075d3535d8","target":"record","created_at":"2026-05-18T00:43:03Z","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":"96c870cba71f0a2b334584e2205b80c8eb01617d0c485335eaddf6207614fa98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"1998-03-23T13:29:16Z","title_canon_sha256":"9282a0f5bfb51d9b6e8dcc2d2333b549674da6630d33242e5071c1026839612a"},"schema_version":"1.0","source":{"id":"math/9803104","kind":"arxiv","version":2}},"canonical_sha256":"21e82cf85063e93d8aade90752294c29219a5aee5fe247d393715a84a32dc5a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21e82cf85063e93d8aade90752294c29219a5aee5fe247d393715a84a32dc5a4","first_computed_at":"2026-05-18T00:43:03.519477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:03.519477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lpTNudc45Df8EVzOwdyBRySIqIFXKdr867qrrps/F56qQSqZBMy4O6ZFaKl83+03oz1UKG0woOcKdnAdB9AZAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:03.520216Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9803104","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7da7c3753ddd55f9eee11f41763e1cbf1cac798d31cb726b58589075d3535d8","sha256:0aa7c1540440985c42ec1c9d1e69c58a95e6b3158d44cfa8a6516901c05857ca"],"state_sha256":"9c8fd9714f6048ffb277d4158ae91b8255635f48369c962acd2efbeaed8da8f3"}