{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-extensions-of-the-jacobson-morozov-theorem","title":"On extensions of the Jacobson-Morozov theorem to even characteristic","arxiv_id":"2401.07303","date":"2024-01-14","proceeding":null,"authors":["David I. Stewart","Adam R. Thomas"],"abstract":"Let G be a simple algebraic group over an algebraically closed field k of characteristic 2. We consider analogues of the Jacobson-Morozov theorem in this setting. More precisely, we classify those nilpotent elements with a simple 3-dimensional Lie overalgebra in $\\mathfrak{g} := \\text{Lie}(G)$ and also those with overalgebras isomorphic to the algebras $\\text{Lie}(\\text{SL}_2)$ and $\\text{Lie}(\\text{PGL}_2)$. This leads us to calculate the dimension of Lie automiser $\\mathfrak{n}_\\mathfrak{g}(k\\cdot e)/\\mathfrak{c}_\\mathfrak{g}(e)$ for all nilpotent orbits; in even characteristic this quantity is very sensitive to isogeny.","url_abs":"https://arxiv.org/abs/2401.07303v1","url_pdf":"https://arxiv.org/pdf/2401.07303v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-extensions-of-the-jacobson-morozov-theorem","repo_url":"https://github.com/davistem/nilpotent_orbits_magma","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2401.07303","atlas_url":"https://app.syntology.ai/?focus=2401.07303","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}