{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TACHTS6FFWB7KKBZGHSOHIOR7W","short_pith_number":"pith:TACHTS6F","schema_version":"1.0","canonical_sha256":"980479cbc52d83f5283931e4e3a1d1fdb3a382d5aeb0ef7660b8d0254de9bc69","source":{"kind":"arxiv","id":"1405.6040","version":2},"attestation_state":"computed","paper":{"title":"Cleft extensions of Koszul twisted Calabi-Yau algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Fred van Oystaeyen, Xiaolan Yu, Yinhuo Zhang","submitted_at":"2014-05-23T12:35:01Z","abstract_excerpt":"Let $H$ be a twisted Calabi-Yau (CY) algebra and $\\sigma$ a 2-cocycle on $H$. Let $A$ be an $N$-Koszul twisted CY algebra such that $A$ is a graded $H^\\sigma$-module algebra. We show that the cleft extension $A#_\\sigma H$ is also a twisted CY algebra. This result has two consequences. Firstly, the smash product of an $N$-Koszul twisted CY algebra with a twisted CY Hopf algebra is still a twisted CY algebra. Secondly, the cleft objects of a twisted CY Hopf algebra are all twisted CY algebras. As an application of this property, we determine which cleft objects of $U(\\mathcal{D},\\lambda)$, a cla"},"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":"1405.6040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-23T12:35:01Z","cross_cats_sorted":[],"title_canon_sha256":"7d4c609d4f9eda88e9f2a067e227a297dd9db9370f3319575eb67ffb892dc382","abstract_canon_sha256":"adf7fcb622b3fdccc4e1ff23df6d6803e28904178ced13cc4620c5f81a602f00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:32.013151Z","signature_b64":"vfgV+MsUxXzaecT+5jI/ZXrQXNLZfEqsM83dMHfQXNMIRBo963XTAUwlwKZwJ6CRjcW9mn2w/dh53FwogxJSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"980479cbc52d83f5283931e4e3a1d1fdb3a382d5aeb0ef7660b8d0254de9bc69","last_reissued_at":"2026-05-18T02:30:32.012722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:32.012722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cleft extensions of Koszul twisted Calabi-Yau algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Fred van Oystaeyen, Xiaolan Yu, Yinhuo Zhang","submitted_at":"2014-05-23T12:35:01Z","abstract_excerpt":"Let $H$ be a twisted Calabi-Yau (CY) algebra and $\\sigma$ a 2-cocycle on $H$. Let $A$ be an $N$-Koszul twisted CY algebra such that $A$ is a graded $H^\\sigma$-module algebra. We show that the cleft extension $A#_\\sigma H$ is also a twisted CY algebra. This result has two consequences. Firstly, the smash product of an $N$-Koszul twisted CY algebra with a twisted CY Hopf algebra is still a twisted CY algebra. Secondly, the cleft objects of a twisted CY Hopf algebra are all twisted CY algebras. As an application of this property, we determine which cleft objects of $U(\\mathcal{D},\\lambda)$, a cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6040","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1405.6040","created_at":"2026-05-18T02:30:32.012789+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.6040v2","created_at":"2026-05-18T02:30:32.012789+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6040","created_at":"2026-05-18T02:30:32.012789+00:00"},{"alias_kind":"pith_short_12","alias_value":"TACHTS6FFWB7","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"TACHTS6FFWB7KKBZ","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"TACHTS6F","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TACHTS6FFWB7KKBZGHSOHIOR7W","json":"https://pith.science/pith/TACHTS6FFWB7KKBZGHSOHIOR7W.json","graph_json":"https://pith.science/api/pith-number/TACHTS6FFWB7KKBZGHSOHIOR7W/graph.json","events_json":"https://pith.science/api/pith-number/TACHTS6FFWB7KKBZGHSOHIOR7W/events.json","paper":"https://pith.science/paper/TACHTS6F"},"agent_actions":{"view_html":"https://pith.science/pith/TACHTS6FFWB7KKBZGHSOHIOR7W","download_json":"https://pith.science/pith/TACHTS6FFWB7KKBZGHSOHIOR7W.json","view_paper":"https://pith.science/paper/TACHTS6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.6040&json=true","fetch_graph":"https://pith.science/api/pith-number/TACHTS6FFWB7KKBZGHSOHIOR7W/graph.json","fetch_events":"https://pith.science/api/pith-number/TACHTS6FFWB7KKBZGHSOHIOR7W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TACHTS6FFWB7KKBZGHSOHIOR7W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TACHTS6FFWB7KKBZGHSOHIOR7W/action/storage_attestation","attest_author":"https://pith.science/pith/TACHTS6FFWB7KKBZGHSOHIOR7W/action/author_attestation","sign_citation":"https://pith.science/pith/TACHTS6FFWB7KKBZGHSOHIOR7W/action/citation_signature","submit_replication":"https://pith.science/pith/TACHTS6FFWB7KKBZGHSOHIOR7W/action/replication_record"}},"created_at":"2026-05-18T02:30:32.012789+00:00","updated_at":"2026-05-18T02:30:32.012789+00:00"}