• Corpus ID: 119285792

# 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}
}
• W. Moens
• Published 5 December 2015
• Mathematics
• arXiv: Rings and Algebras
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.

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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