{"paper":{"title":"On the Cohomology of the Lie Superalgebra of Contact Vector Fields on $S^{1|2}$","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Boujemaa Agrebaoui, Nizar Ben Fraj, Salem Omri","submitted_at":"2006-03-23T08:00:07Z","abstract_excerpt":"We investigate the first cohomology space associated with the embedding of the Lie superalgebra $\\cK(2)$ of contact vector fields on the (1,2)-dimensional supercircle $S^{1\\mid 2}$ in the Lie superalgebra $\\cS\\Psi \\cD \\cO(S^{1\\mid 2})$ of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger, we show that this space is ten-dimensional with only even cocycles and we give explicit expressions of the basis cocycles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0603057","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"}