{"paper":{"title":"A method to find generators of a semi-simple Lie group via the topology of its flag manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AT","authors_text":"Ariane Luzia dos Santos, Luiz A. B. San Martin","submitted_at":"2015-04-27T20:34:03Z","abstract_excerpt":"In this paper we continue to develop the topological method started in Santos-San Martin \\cite{ariasm} to get semigroup generators of semi-simple Lie groups. Consider a subset $\\Gamma \\subset G$ that contains a semi-simple subgroup $G_{1}$ of $G$. Then $\\Gamma $ generates $G$ if $\\mathrm{Ad}\\left( \\Gamma \\right) $ generates a Zariski dense subgroup of the algebraic group $\\mathrm{Ad}\\left( G\\right) $. The proof is reduced to check that some specific closed orbits of $G_{1}$ in the flag manifolds of $G$ are not trivial in the sense of algebraic topology. Here, we consider three different cases "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07271","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"}