On Dynkin gradings in simple Lie algebras

2018/06/03 by Elashvili, A. G., Jibladze, M., Kac, V. G.
#17B08 #17B10 #17B20 #17B22 #17B25 #17B70 #17B80 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1806.00893

Abstract

In this paper we study gradings on simple Lie algebras arising from nilpotent elements. Specifically, we investigate abelian subalgebras which are degree 1 homogeneous with respect to these gradings. We show that for each odd nilpotent element there always exists canonically associated "strictly" odd nilpotent element, which allows us to reduce our investigations to the latter.

Related

• Dynkin abelianisations of Lie algebras of exceptional type
• Arithmetically-free group-gradings of Lie algebras
• Gradings by Groups on Graded Cartan Type Lie Algebras
• Special pure gradings on simple Lie algebras of types E₆, E₇, E₈
• Graded simple Lie algebras and graded simple representations