Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

An analogue of the Jacobson-Morozov theorem for Lie algebras of reductive groups of good characteristics


Author: Alexander Premet
Journal: Trans. Amer. Math. Soc. 347 (1995), 2961-2988
MSC: Primary 17B10; Secondary 17B50, 20G05
MathSciNet review: 1290730
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathfrak{g}$ be the Lie algebra of a connected reductive group $ G$ over an algebraically closed field of characteristic $ p > 0$. Suppose that $ {G^{(1)}}$ is simply connected and $ p$ is good for the root system of $ G$. Given a one-dimensional torus $ \lambda \subset G$ let $ \mathfrak{g}(\lambda ,1)$ denote the weight component of $ {\text{Ad(}}\lambda {\text{)}}$ corresponding to weight $ i \in X(\lambda ) \cong \mathbb{Z}$. It is proved in the paper that, for any nonzero nilpotent element $ e \in \mathfrak{g}$, there is a one-dimentional torus $ {\lambda _e} \subset G$ such that $ e \in \mathfrak{g}({\lambda _e},2)$ and $ {\text{Ker}}{\text{ad}}e \subseteq { \oplus _{i \geqslant 0}}\mathfrak{g}({\lambda _e},i)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 17B10, 17B50, 20G05

Retrieve articles in all journals with MSC: 17B10, 17B50, 20G05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1290730-7
PII: S 0002-9947(1995)1290730-7
Keywords: Nilpotent element, Lie algebra, reductive group, prime characteristic
Article copyright: © Copyright 1995 American Mathematical Society