A note on the structure of graded Lie algebras

2015/12/05 by Moens, Wolfgang Alexander
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1512.01697

Abstract

Consider a finite-dimensional, complex Lie algebra G and a semi-simple automorphism α. 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 α and the dimension of the space of fixed-points. This is an extension of classical theorems by Kreknin, Shalev and Jacobson.

Related

• The Levi Decomposition of a Graded Lie Algebra
• L-prolongations of graded Lie algebras
• Constructing Graded Lie Algebras
• On Levi extensions of nilpotent Lie algebras
• Deformations of graded Lie algebras and symplectic structures