# Formal group law of an algebraic group

From Groupprops

## Definition

Suppose is an algebraic group over a field . The **formal group law** of is a formal group law over obtained by taking coordinates in an affine neighborhood of the identity, setting the identity element as the origin for the coordinates.

## Facts

- The formal group law of an algebraic group is the same as the formal group law of its connected component of identity. In particular, the formal group law depends only on the connected component of identity.