Unipotent algebraic group

A unipotent algebraic group is built from unipotent elements. A unipotent algebraic group is an affine algebraic group all of whose elements are unipotent. The Kolchin theorem embeds it into an upper unitriangular group.

It is the largest connected normal unipotent subgroup of a linear algebraic group. A connected reductive algebraic group has trivial unipotent radical. The subgroup $1+J(E)$ of a finite-dimensional algebra's unit group is closed, connected and unipotent.

Every unipotent algebraic subgroup of ${\mathrm{GL}}_n$ is conjugate to a subgroup of the upper unitriangular group. The filtration by vanishing initial superdiagonals then proves that every unipotent algebraic group is a nilpotent group.