{"paper":{"title":"Classification of the maximal subalgebras of exceptional Lie algebras over fields of good characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.RA","authors_text":"Alexander Premet, David I. Stewart","submitted_at":"2017-11-19T09:28:15Z","abstract_excerpt":"Let $G$ be an exceptional simple algebraic group over an algebraically closed field $k$ and suppose that the characteristic $p$ of $k$ is a good prime for $G$. In this paper we classify the maximal Lie subalgebras $\\mathfrak{m}$ of the Lie algebra $\\mathfrak{g}={\\rm Lie}(G)$. Specifically, we show that one of the following holds: $\\mathfrak{m}={\\rm Lie}(M)$ for some maximal connected subgroup $M$ of $G$, or $\\mathfrak{m}$ is a maximal Witt subalgebra of $\\mathfrak{g}$, or $\\mathfrak{m}$ is a maximal $\\it{\\mbox{exotic semidirect product}}$. The conjugacy classes of maximal connected subgroups o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06988","kind":"arxiv","version":4},"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"}