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

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&#...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Pengelly, Rachel, Testerman, Donna M
Format: Article
Language:English
Subjects:
Algebra
Fields (mathematics)
Group theory
Lie groups
Subgroups
Online Access:Get full text
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Summary: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
ISSN:2331-8422