{"paper":{"title":"The Binary $\\mathfrak{aff}(n|1)$-Invariant Differential Operators On Weighted Densities On The Superspace $\\mathbb{R}^{1|n}$ And $\\mathfrak{aff}(n|1)$-Relative Cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Khaled Basdouri, Salem Omri, Wissal Swilah","submitted_at":"2018-02-03T15:22:58Z","abstract_excerpt":"We consider the $\\mathfrak{aff}(n|1)-$module structure on the spaces of differential bilinear operators acting on the superspaces of weighted densities. We classify $\\mathfrak{aff}(n|1)-$invariant binary differential operators acting on the spaces of weighted densities. This result allows us to compute the first $\\mathfrak{aff}(n|1)-$relative differential cohomology of $\\mathcal{K}(n)$ with coefficients in the superspace of linear differential operators acting on the superspaces of weighted densities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02433","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"}