Unipotent element of an affine algebraic group

An element of an affine algebraic group is unipotent when its image in one, equivalently every, faithful finite-dimensional representation has every eigenvalue equal to one.

A square matrix $U$ is unipotent when $U-I$ is nilpotent. Over an algebraically closed field, this is equivalent to all eigenvalues being one. If $j$ belongs to a nilpotent ideal of an operator algebra, $I+j$ is a unipotent matrix. This realizes the radical factor in the Levi decomposition of a quiver automorphism group.