{"paper":{"title":"Differential Operators on the Weighted Densities on the Supercircle $S^{1|n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mabrouk Ben Ammar, Nader Belghith, Nizar Ben Fraj","submitted_at":"2013-06-01T12:54:08Z","abstract_excerpt":"Over the $(1,n)$-dimensional real supercircle, we consider the $\\mathcal{K}(n)$-modules of linear differential operators, $\\frak{D}^n_{\\lambda,\\mu}$, acting on the superspaces of weighted densities, where $\\mathcal{K}(n)$ is the Lie superalgebra of contact vector fields. We give, in contrast to the classical setting, a classification of these modules for $n=1$. We also prove that $\\frak{D}^{n}_{\\lambda,\\mu}$ and $\\frak{D}_{\\rho,\\nu}^{n}$ are isomorphic for $\\rho=\\frac{2-n}{2}-\\mu$ and $\\nu=\\frac{2-n}{2}-\\lambda$. This work is the simplest superization of a result by Gargoubi and Ovsienko [Modu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0101","kind":"arxiv","version":3},"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"}