Papers › On extensions of the Jacobson-Morozov theorem to even characteristic
On extensions of the Jacobson-Morozov theorem to even characteristic
David I. Stewart, Adam R. Thomas
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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 𝔤 := 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 𝔫_𝔤(k·e)/𝔠_𝔤(e) for all nilpotent orbits; in even characteristic this quantity is very sensitive to isogeny.
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