Additive formal group law

From Groupprops
Jump to: navigation, search

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.