Lie algebra of a formal group law

Definition
Suppose $$F$$ is a $$n$$-dimensional defining ingredient::formal group law over a commutative unital ring $$R$$. The Lie algebra of $$F$$ is defined as the following Lie algebra $$L$$:


 * Additively, it is a free module $$R^n$$.
 * For any two elements $$x = (x_1,x_2,\dots,x_n)$$ and $$y = (y_1,y_2,\dots,y_n)$$, we define $$[x,y]$$ as:

$$\! [x,y] := F_2(x,y) - F_2(y,x)$$

where $$F_2$$ is the degree two part of the expression for $$F$$.