{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2FFPFAUHBAYNFRX2W7MPX6UK6S","short_pith_number":"pith:2FFPFAUH","schema_version":"1.0","canonical_sha256":"d14af282870830d2c6fab7d8fbfa8af4a1d14478fe1892259c0fcc9ab8496518","source":{"kind":"arxiv","id":"1712.09202","version":2},"attestation_state":"computed","paper":{"title":"Biderivations and commutative post-Lie algebra structures on the Lie algebra W(a,b)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Xiaomin Tang","submitted_at":"2017-12-26T08:03:08Z","abstract_excerpt":"For $a,b\\in \\mathbb{C}$, the Lie algebra $\\mathcal{W}(a,b)$ is the semidirect product of the Witt algebra and a module of the intermediate series. In this paper, all biderivations of $\\mathcal{W}(a,b)$ are determined. Surprisingly, these Lie algebras have symmetric (and skewsymmetric) non-inner biderivations. As an applications, commutative post-Lie algebra structures on $\\mathcal{W}(a,b)$ are obtained."},"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":"1712.09202","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-26T08:03:08Z","cross_cats_sorted":[],"title_canon_sha256":"7a5774ef6384dd42197c3e1b1b562aa730fff71e24687c10cbd979c4d5c83ead","abstract_canon_sha256":"3ee24de758ea852895aa7fd8d9a91933321bb8bbdee6d26f70e869ae5c2fc39d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:53.354647Z","signature_b64":"vNW5FQnvB6Bpmcb83PVh2G8o3G/dV896RMeFuFTfNChDeEsLb/MQHJ8G7HKMvaKID8dNp4SpxEfqMNN4Qgu1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d14af282870830d2c6fab7d8fbfa8af4a1d14478fe1892259c0fcc9ab8496518","last_reissued_at":"2026-05-18T00:26:53.353824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:53.353824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biderivations and commutative post-Lie algebra structures on the Lie algebra W(a,b)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Xiaomin Tang","submitted_at":"2017-12-26T08:03:08Z","abstract_excerpt":"For $a,b\\in \\mathbb{C}$, the Lie algebra $\\mathcal{W}(a,b)$ is the semidirect product of the Witt algebra and a module of the intermediate series. In this paper, all biderivations of $\\mathcal{W}(a,b)$ are determined. Surprisingly, these Lie algebras have symmetric (and skewsymmetric) non-inner biderivations. As an applications, commutative post-Lie algebra structures on $\\mathcal{W}(a,b)$ are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09202","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":"1712.09202","created_at":"2026-05-18T00:26:53.353957+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.09202v2","created_at":"2026-05-18T00:26:53.353957+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09202","created_at":"2026-05-18T00:26:53.353957+00:00"},{"alias_kind":"pith_short_12","alias_value":"2FFPFAUHBAYN","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2FFPFAUHBAYNFRX2","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2FFPFAUH","created_at":"2026-05-18T12:30:55.937587+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/2FFPFAUHBAYNFRX2W7MPX6UK6S","json":"https://pith.science/pith/2FFPFAUHBAYNFRX2W7MPX6UK6S.json","graph_json":"https://pith.science/api/pith-number/2FFPFAUHBAYNFRX2W7MPX6UK6S/graph.json","events_json":"https://pith.science/api/pith-number/2FFPFAUHBAYNFRX2W7MPX6UK6S/events.json","paper":"https://pith.science/paper/2FFPFAUH"},"agent_actions":{"view_html":"https://pith.science/pith/2FFPFAUHBAYNFRX2W7MPX6UK6S","download_json":"https://pith.science/pith/2FFPFAUHBAYNFRX2W7MPX6UK6S.json","view_paper":"https://pith.science/paper/2FFPFAUH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.09202&json=true","fetch_graph":"https://pith.science/api/pith-number/2FFPFAUHBAYNFRX2W7MPX6UK6S/graph.json","fetch_events":"https://pith.science/api/pith-number/2FFPFAUHBAYNFRX2W7MPX6UK6S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2FFPFAUHBAYNFRX2W7MPX6UK6S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2FFPFAUHBAYNFRX2W7MPX6UK6S/action/storage_attestation","attest_author":"https://pith.science/pith/2FFPFAUHBAYNFRX2W7MPX6UK6S/action/author_attestation","sign_citation":"https://pith.science/pith/2FFPFAUHBAYNFRX2W7MPX6UK6S/action/citation_signature","submit_replication":"https://pith.science/pith/2FFPFAUHBAYNFRX2W7MPX6UK6S/action/replication_record"}},"created_at":"2026-05-18T00:26:53.353957+00:00","updated_at":"2026-05-18T00:26:53.353957+00:00"}