A note on the structure of graded Lie algebras
@article{Moens2015ANO,
title={A note on the structure of graded Lie algebras},
author={Wolfgang Alexander Moens},
journal={arXiv: Rings and Algebras},
year={2015}
}Consider a finite-dimensional, complex Lie algebra G and a semi-simple automorphism {\alpha}. This note aims to give a short and simple proof for explicit upper bounds for the derived length of the radical R and the rank of a Levi complement G/R in terms of the number of eigenvalues of {\alpha} and the dimension of the space of fixed-points. This is an extension of classical theorems by Kreknin, Shalev and Jacobson.
References
SHOWING 1-10 OF 13 REFERENCES
A note on automorphisms of Lie algebras
- Mathematics
- 1962
In a beautiful paper which appeared in 1939 ([4]), F. Gantmacher made a thorough study of automorphisms of semi-simple Lie algebras over the field of complex numbers. Among other things, he defined…
Automorphisms of finite groups of bounded rank
- Mathematics
- 1993
LetG be a finite group admitting an automorphismα withm fixed points. Suppose every subgroup ofG isr-generated. It is shown that (1)G has a characteristic soluble subgroupH whose index is bounded in…
Nilpotent Groups and Their Automorphisms
- Mathematics
- 1993
The fact that nilpotent groups are close to being commutative means that it is possible to apply linear methods to their study. In this volume, based on a special course given by the author at…
A note on automorphisms and derivations of Lie algebras
- Mathematics
- 1955
In a recent paper Borei and Serre proved the theorem: If \( \mathfrak{L} \) is a Lie algebra of characteristic 0 and \( \mathfrak{L} \) has an automorphism of prime period without fixed points ≠ 0,…
p-automorphisms of finite p-groups
- Mathematics
- 1998
Preface Introduction 1. Preliminaries 2. Automorphisms and their fixed points 3. Nilpotent and soluble groups 4. Finite p-groups 5. Lie rings 6. Associated Lie rings 7. Regular automorphisms of Lie…
On p -automorphisms of finite p -groups
- Mathematics
- 1979
Following your need to always fulfil the inspiration to obtain everybody is now simple. Connecting to the internet is one of the short cuts to do. There are so many sources that offer and connect us…
Sur certains sous-groupes des groupes de Lie compacts
- Mathematics
- 1953
On sai t que t o u t sous-groupe ab~lien connexe H d ' u n groupe de Lie compac t G est contenu dans u n tore m a x i m a l de G; pa r contre cet te propri~t~ peu t ~tre en d~faut pour un sous-groupe…