Arithmetically-free group-gradings of Lie algebras: II

[摘要] We study Lie algebras L that are graded by an arbitrary group (G, *) and have finite support, X. We show that L is nilpotent of vertical bar X vertical bar-bounded class if X is arithmetically-free. Conversely: if a finite subset Y of G is not arithmetically-free, then Y supports the grading of a non-nilpotent Lie algebra. (C) 2017 Elsevier Inc. All rights reserved.

[发布日期] 2017-12-15

[关键词] Lie algebras;Group-gradings;Nilpotent;Higman;Identities in algebras