{"paper":{"title":"Diameter bounds for finite simple Lie algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.GR","math.RT"],"primary_cat":"math.RA","authors_text":"Marco Barbieri, Matev\\v{z} Mi\\v{s}\\v{c}i\\v{c}, Urban Jezernik","submitted_at":"2025-09-18T18:43:19Z","abstract_excerpt":"We prove strong and explicit diameter bounds for finite simple Lie algebras, which parallel Babai's conjecture for finite simple groups. Specifically, we show that any nonabelian finite simple Lie algebra $\\mathfrak{g}$ over $\\mathbf{F}_p$ has diameter $O((\\log |\\mathfrak{g}|)^D)$ for $D \\approx 3.11$ with respect to any generating set. For absolutely simple classical Lie algebras over $\\mathbf{F}_p$, we establish the sharper bound $O(\\log |\\mathfrak{g}|)$ when the Lie type is fixed and the generators are chosen uniformly at random."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.15351","kind":"arxiv","version":3},"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/2509.15351/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"}