{"paper":{"title":"A simple proof of the first Kac-Weisfeiler conjecture for algebraic Lie algebras in large characteristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Akaki Tikaradze","submitted_at":"2018-11-26T05:27:24Z","abstract_excerpt":"Given a Lie algebra $\\mathfrak{g}$ of an algebraic group over a ring $S,$ we show that the first Kac-Weisfeiler conjecture holds for reductions of $\\mathfrak{g} \\mod p$ for large enough primes $p,$ reproving a recent result of Martin, Stewart and Topley. As a byproduct of our proof, we show that the center of the skew field of fractions of the the enveloping algebra $\\mathfrak{U}\\mathfrak{g}_{k}$ for a field $k$ of characteristic $p>>0$ is generated by the $p$-center and by the reduction $\\mod p$ of the center of the fraction skew field of $\\mathfrak{U}\\mathfrak{g}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10182","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"}