Every Lie ring is naturally isomorphic to its opposite Lie ring via the negative map

Statement
Let $$L$$ be a Lie ring with Lie bracket denoted by $$[,]$$. The opposite Lie ring $$L^{op}$$ is defined as the Lie ring with the same underlying set and additive group, and the bracket $$\{, \}$$ defined as:

$$\{ x, y \} = [y,x]$$.

Then, the map from $$L$$ to $$L^{op}$$ given by $$x \mapsto -x$$ is an isomorphism of Lie rings.

Related facts

 * Every group is naturally isomorphic to its opposite group