Arithmetically-free group-gradings of Lie algebras: II

2016/05/17 by Moens, Wolfgang Alexander
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1605.05090

Abstract

We study group-graded Lie algebras L with finite support X. We show that L is nilpotent of |X|-bounded class if X is arithmetically-free. Conversely: we show that Y supports the grading of a non-nilpotent Lie algebra if Y is not arithmetically-free.

Related

• Arithmetically-free group-gradings of Lie algebras
• Gradings for nilpotent Lie algebras
• A Lie grading which is not a semigroup grading
• Gradings on Lie algebras with applications to infra-nilmanifolds
• Gradings by Groups on Graded Cartan Type Lie Algebras