{"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"}