On extensions of the Jacobson-Morozov theorem to even characteristic

2024/01/14 by David I. Stewart, Stewart, David I., Adam R. Thomas +1
Mathematics · #17B45 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2401.07303

openalex publication_date 2024/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathfrakg := Lie(G) and also those with overalgebras isomorphic to the algebras Lie(SL₂) and Lie(PGL₂). This leads us to calculate the dimension of Lie automiser \mathfrakn_\mathfrakg(k⋅ e)/\mathfrakc_\mathfrakg(e) for all nilpotent orbits; in even characteristic this quantity is very sensitive to isogeny.

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