Additive formal group law

Definition

One-dimensional additive formal group law

Suppose $R$ is a commutative unital ring. The one-dimensional additive formal group law over $R$ is the formal group law given by the power series:

$F(x,y)=x+y$

It is an example of a commutative formal group law.

Higher-dimensional formal group law

Suppose $R$ is a commutative unital ring. The $n$-dimensional additive formal group law over $R$ is the formal group law given by the following collection of power series:

$F_i(x_1,x_2,\dots ,x_n,y_1,y_2,\dots ,y_n)=x_i+y_i,1\le i\le n$

More compactly, this is written as:

$F(x,y)=x+y$

where $x=(x_1,x_2,\dots ,x_n)$ and $y=(y_1,y_2,\dots ,y_n)$.

This is an example of a commutative formal group law.