{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:537NTYCHMVNHGHEYJLJF4O7MFN","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":"0802134faafd533b659c4d6b279cea502730e7272420ff918aa9d29639143d68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-12-31T18:17:58Z","title_canon_sha256":"433b0562b7f987642fe496467b72190f816ca38872a29cac603c20fd1c0d180c"},"schema_version":"1.0","source":{"id":"1701.00153","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00153","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00153v1","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00153","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"537NTYCHMVNH","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"537NTYCHMVNHGHEY","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"537NTYCH","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:23e21b650648341f491746dd20db9df86dcc708798c3fb59ebbb74dfc254c2b8","target":"graph","created_at":"2026-05-18T00:53:36Z","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":"We show that the definition of unrolled Hopf algebras can be naturally extended to the Nichols algebra $\\mathcal{B}$ of a Yetter-Drinfeld module $V$ on which a Lie algebra $\\mathfrak g$ acts by biderivations. Specializing to Nichols algebras of diagonal type, we find unrolled versions of the small, the De Concini-Procesi and the Lusztig divided power quantum group, respectively.","authors_text":"Christoph Schweigert, Nicol\\'as Andruskiewitsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-12-31T18:17:58Z","title":"On unrolled Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00153","kind":"arxiv","version":1},"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:e1af054221795ed16bdab2031cd04362505ea0b7843e2a51e4fe0b8470e9e810","target":"record","created_at":"2026-05-18T00:53:36Z","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":"0802134faafd533b659c4d6b279cea502730e7272420ff918aa9d29639143d68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-12-31T18:17:58Z","title_canon_sha256":"433b0562b7f987642fe496467b72190f816ca38872a29cac603c20fd1c0d180c"},"schema_version":"1.0","source":{"id":"1701.00153","kind":"arxiv","version":1}},"canonical_sha256":"eefed9e047655a731c984ad25e3bec2b5ae8577f321779217f59eae9c11ca7fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eefed9e047655a731c984ad25e3bec2b5ae8577f321779217f59eae9c11ca7fc","first_computed_at":"2026-05-18T00:53:36.230157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:36.230157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xVma1x6rGyAejfHzStbLGVPBEOoH598hCfqmbv1zCKXT5mk3GHNIExiegEg0DL6r9q+Blx66gjxK4ToAeW35AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:36.230555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00153","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1af054221795ed16bdab2031cd04362505ea0b7843e2a51e4fe0b8470e9e810","sha256:23e21b650648341f491746dd20db9df86dcc708798c3fb59ebbb74dfc254c2b8"],"state_sha256":"ba9d99934c72ddf92b839c639fc5989430338a98e5e874461bda0683fc44fefa"}