{"paper":{"title":"The Binary Invariant Differential Operators on Weighted Densities on the superspace $\\mathbb{R}^{1|n}$ and Cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.RT","authors_text":"Mabrouk Ben Ammar, Nizar Ben Fraj, Salem Omri","submitted_at":"2009-12-27T12:58:30Z","abstract_excerpt":"Over the $(1,n)$-dimensional real superspace, $n>1$, we classify\n  $\\mathcal{K}(n)$-invariant binary differential operators acting on the superspaces of weighted densities, where $\\mathcal{K}(n)$ is the Lie superalgebra of contact vector fields. This result allows us to compute the first differential cohomology of %the Lie superalgebra $\\mathcal{K}(n)$ with coefficients in the superspace of linear differential operators acting on the superspaces of weighted densities--a superisation of a result by Feigin and Fuchs. We explicitly give 1-cocycles spanning these cohomology spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.5070","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"}