2-Lazard-dividable Lie ring
Definition
A Lie ring with bracket is termed a 2-Lazard-dividable Lie ring or a Lie ring whose bracket is the double of a Lie bracket if can be equipped with a Lie ring structure with the same additive group and a Lie bracket such that:
![{\displaystyle [,]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f04349be7aa458edb6f1ab423189a8455c6e21f7)
![{\displaystyle [x,y]=2\{x,y\}\ \forall \ x,y\in L}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d765339ffe7aabf6d0b1628ce1ef65eee919fa52)
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 |