{"paper":{"title":"The Subalgebras of the Real Forms of \\(\\mathfrak{sl}_3(\\mathbb{C})\\)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrew Douglas, Willem A. de Graaf","submitted_at":"2025-02-02T14:30:15Z","abstract_excerpt":"We classify the subalgebras of the real forms the complex linear algebra $\\mathfrak{sl}_3(\\mathbb{C})$, namely the real special linear algebra $\\mathfrak{sl}_3(\\mathbb{R})$, the special unitary algebra $\\mathfrak{su}(3)$, and the generalized special unitary algebra $\\mathfrak{su}(2,1)$. Our approach applies Galois cohomology to the known classification of complex subalgebras of $\\mathfrak{sl}_3(\\mathbb{C})$. The subalgebras of $\\mathfrak{sl}_3(\\mathbb{R})$ were previously classified by Winternitz using different techniques. We recover this classification using our cohomological approach and am"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.00810","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.00810/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}