2-Lazard-dividable Lie ring

From Groupprops

Definition

A Lie ring L with bracket [,] is termed a 2-Lazard-dividable Lie ring or a Lie ring whose bracket is the double of a Lie bracket if L can be equipped with a Lie ring structure with the same additive group and a Lie bracket {,} such that:

[x,y]=2{x,y}x,yL

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
uniquely 2-divisible Lie ring
abelian Lie ring
Baer Lie ring
Lie ring whose bracket is the double of a Lie bracket giving nilpotency class two