{"paper":{"title":"Homogeneous irreducible supermanifolds and graded Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"A. Santi, D. V. Alekseevsky","submitted_at":"2015-11-22T19:29:44Z","abstract_excerpt":"A depth one grading $\\mathfrak{g}= \\mathfrak{g}^{-1}\\oplus \\mathfrak{g}^0 \\oplus \\mathfrak{g}^1 \\oplus \\cdots \\oplus \\mathfrak{g}^{\\ell}$ of a finite dimensional Lie superalgebra $\\mathfrak{g}$ is called nonlinear irreducible if the isotropy representation $\\mathrm{ad}_{\\mathfrak{g}^0}|_{\\mathfrak{g}^{-1}}$ is irreducible and $\\mathfrak{g}^1 \\neq (0)$. An example is the full prolongation of an irreducible linear Lie superalgebra $\\mathfrak{g}^0 \\subset \\mathfrak{gl}(\\mathfrak{g}^{-1})$ of finite type with non-trivial first prolongation. We prove that a complex Lie superalgebra $\\mathfrak{g}$ w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07055","kind":"arxiv","version":2},"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"}