English

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

Group Theory 2023-11-22 v1

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

Keywords

Cite

@article{arxiv.2311.12512,
  title  = {Unicity of A1-subgroups associated to unipotent elements in simple algebraic groups},
  author = {Rachel Pengelly and Donna M. Testerman},
  journal= {arXiv preprint arXiv:2311.12512},
  year   = {2023}
}