Class two Lie cring

Definition
A class two Lie cring is an abelian group $$L$$ (denoted additively) equipped with an additional binary operation $$*$$ satisfying the following additional conditions:

Equivalently, a class two Lie cring is a Lie cring satisfying the additional condition that $$a * (b * c) = 0$$ for all $$a,b,c$$ in the Lie cring.

Facts

 * Double of class two Lie cring is class two Lie ring