{"paper":{"title":"Total cohomology of solvable Lie algebras and linear deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Leandro Cagliero, Paulo Tirao","submitted_at":"2014-03-17T12:50:42Z","abstract_excerpt":"Given a finite dimensional Lie algebra $\\mathfrak{g}$, let $\\Gamma_\\circ(\\mathfrak{g})$ be the set of irreducible $\\mathfrak{g}$-modules with non-vanishing cohomology. We prove that a $\\mathfrak{g}$-module $V$ belongs to $\\Gamma_\\circ(\\mathfrak{g})$ only if $V$ is contained in the exterior algebra of the solvable radical $\\mathfrak{s}$ of $\\mathfrak{g}$, showing in particular that $\\Gamma_\\circ(\\mathfrak{g})$ is a finite set and we deduce that $H^*(\\mathfrak{g},V)$ is an $L$-module, where $L$ is a fixed subgroup of the connected component of $\\operatorname{Aut}(\\mathfrak{g})$ which contains a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4083","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"}