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In this note, using the method of reduction on $\\mathbb{Z}$-gradations, we determine the derivation space $\\mathrm{Der}(\\mathcal{W}, W_{\\bar{1}})$ from $\\mathcal{W}$ into $W_{\\bar{1}} $ and the derivation space $\\mathrm{Der}(\\mathcal{S}, W_{\\bar{1}})$ from $\\mathcal{S}$ into $W_{\\bar{1}}. $ In particular, the derivation space $\\mathrm{Der}(\\mathcal{S}, S_{\\bar{1}})$ is determined."},"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":"math/0509177","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2005-09-08T01:03:33Z","cross_cats_sorted":[],"title_canon_sha256":"af8273d11ef0c3ae8e90d141efd4ebc33731e51da02ac64ad9be002c7de7c26a","abstract_canon_sha256":"9604de1df6df113a1bc33fca608d967c3dd45231017c19136a226f5a182c0f20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:56.213707Z","signature_b64":"+xteQmwJiNDfCv0gPi1N+vOS5MPreRBszbnLI7jnXVQtylpke9uaD5/XlL+ArYGUcdv7nwhSNPo9Cer+QGG6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a6d03fb9e2fefc1add6da651e3e88a7621e740650c7b6a87aec67f7850c7719","last_reissued_at":"2026-05-18T00:09:56.212835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:56.212835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Derivations from the even parts into the odd parts for Lie superalgebras W and S","license":"","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Baoling Liu, Wende Liu","submitted_at":"2005-09-08T01:03:33Z","abstract_excerpt":"Let $\\mathcal{W}$ and $\\mathcal{S}$ denote the even parts of the general Witt superalgebra $W$ and the special superalgebra $S$ over a field of characteristic $ p>3,$ respectively. In this note, using the method of reduction on $\\mathbb{Z}$-gradations, we determine the derivation space $\\mathrm{Der}(\\mathcal{W}, W_{\\bar{1}})$ from $\\mathcal{W}$ into $W_{\\bar{1}} $ and the derivation space $\\mathrm{Der}(\\mathcal{S}, W_{\\bar{1}})$ from $\\mathcal{S}$ into $W_{\\bar{1}}. $ In particular, the derivation space $\\mathrm{Der}(\\mathcal{S}, S_{\\bar{1}})$ is determined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509177","kind":"arxiv","version":1},"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":"math/0509177","created_at":"2026-05-18T00:09:56.212958+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0509177v1","created_at":"2026-05-18T00:09:56.212958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509177","created_at":"2026-05-18T00:09:56.212958+00:00"},{"alias_kind":"pith_short_12","alias_value":"JJWQH646F7X4","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"JJWQH646F7X4DLOW","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"JJWQH646","created_at":"2026-05-18T12:25:53.335082+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/JJWQH646F7X4DLOW3JSR4PUIU5","json":"https://pith.science/pith/JJWQH646F7X4DLOW3JSR4PUIU5.json","graph_json":"https://pith.science/api/pith-number/JJWQH646F7X4DLOW3JSR4PUIU5/graph.json","events_json":"https://pith.science/api/pith-number/JJWQH646F7X4DLOW3JSR4PUIU5/events.json","paper":"https://pith.science/paper/JJWQH646"},"agent_actions":{"view_html":"https://pith.science/pith/JJWQH646F7X4DLOW3JSR4PUIU5","download_json":"https://pith.science/pith/JJWQH646F7X4DLOW3JSR4PUIU5.json","view_paper":"https://pith.science/paper/JJWQH646","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0509177&json=true","fetch_graph":"https://pith.science/api/pith-number/JJWQH646F7X4DLOW3JSR4PUIU5/graph.json","fetch_events":"https://pith.science/api/pith-number/JJWQH646F7X4DLOW3JSR4PUIU5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JJWQH646F7X4DLOW3JSR4PUIU5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JJWQH646F7X4DLOW3JSR4PUIU5/action/storage_attestation","attest_author":"https://pith.science/pith/JJWQH646F7X4DLOW3JSR4PUIU5/action/author_attestation","sign_citation":"https://pith.science/pith/JJWQH646F7X4DLOW3JSR4PUIU5/action/citation_signature","submit_replication":"https://pith.science/pith/JJWQH646F7X4DLOW3JSR4PUIU5/action/replication_record"}},"created_at":"2026-05-18T00:09:56.212958+00:00","updated_at":"2026-05-18T00:09:56.212958+00:00"}