{"paper":{"title":"Cohomology of $\\mathfrak {osp}(1|2)$ acting on linear differential operators on the supercircle $S^{1|1}","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Imed Basdouri, Mabrouk Ben Ammar","submitted_at":"2007-09-12T07:48:33Z","abstract_excerpt":"We compute the first cohomology spaces $H^1(\\mathfrak{osp}(1|2);\\mathfrak{D}_{\\lambda,\\mu})$ ($\\lambda, \\mu\\in\\mathbb{R}$) of the Lie superalgebra $\\mathfrak{osp}(1|2)$ with coefficients in the superspace $\\mathfrak{D}_{\\lambda,\\mu}$ of linear differential operators acting on weighted densities on the supercircle $S^{1|1}$. The structure of these spaces was conjectured in \\cite{gmo}. In fact, we prove here that the situation is a little bit more complicated. (To appear in LMP.)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.1768","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"}