{"paper":{"title":"The classification of the cyclic $\\mathfrak{sl}(n+1)\\ltimes \\mathbbm{C}^{n+1}$--modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Paolo Casati","submitted_at":"2015-08-28T13:33:15Z","abstract_excerpt":"In this paper we classify all the cyclic finite dimensional indecomposable\\\\ modules of the perfect Lie algebras $\\mathfrak{sl}(n+1)\\ltimes \\mathbbm{C}^{n+1}$, given by the semidirect sum of the simple Lie algebra $A_n$ with its standard representation. Furthermore, using the embeddings of the Lie algebras $\\mathfrak{sl}(n+1)\\ltimes \\mathbbm{C}^{n+1}$ in $\\mathfrak{sl}(n+2)$, we show that any finite dimensional irreducible module of $\\mathfrak{sl}(n+2)$ restricted to $\\mathfrak{sl}(n+1)\\ltimes \\mathbbm{C}^{n+1}$ is a cyclic module and that any cyclic $\\mathfrak{sl}(n+1)\\ltimes \\mathbbm{C}^{n+1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07203","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"}