Arithmetically-free group-gradings of Lie algebras: II
Wolfgang Alexander Moens
TL;DR
This paper investigates the structure of group-graded Lie algebras with finite support, establishing conditions under which they are nilpotent based on the arithmetically-free property of the grading support.
Contribution
It provides a characterization linking arithmetically-free supports to nilpotency of Lie algebras, extending previous results in the theory of graded Lie algebras.
Findings
Nilpotency of Lie algebras with arithmetically-free support is bounded by the support size.
Non-nilpotent Lie algebras can have support not arithmetically-free.
Arithmetically-free supports are necessary for nilpotency in group-graded Lie algebras.
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.
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