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arXiv · 2311.12512

Unicity of A1-subgroups associated to unipotent elements in simple algebraic groups

Rachel Pengelly·Donna M. Testerman
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Abstract

Let k be an algebraically closed field of positive characteristic and G a simple algebraic group defined over k. Under the assumption that the characteristic is a good prime for G, we determine a maximal G-stable subvariety U' of the variety of unipotent elements of G such that for all u in U' any two A1-subgroups of G containing u are G-conjugate. This result establishes to what degree an analogue of the Jacobson-Morozov theorem for Lie algebras is valid for simple algebraic groups defined over fields of (good) positive characteristic

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Rachel Pengelly, Donna M. Testerman. 2023-11-21. Unicity of A1-subgroups associated to unipotent elements in simple algebraic groups. https://arxiv.org/abs/2311.12512

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