Unipotent algebraic group

Definition

Definition for linear algebraic group

A unipotent linear algebraic group is a linear algebraic group in which every element is a unipotent element.

Definition for affine algebraic group

A unipotent affine algebraic group is an affine algebraic group that becomes a unipotent linear algebraic group under the natural interpretation of the affine algebraic group as a linear algebraic group.

Relation with group properties

In the finite-dimensional case, any unipotent algebraic group is a nilpotent group, and in the linear case, the order of matrices used (i.e., the dimension of the vector space being acted upon) is an upper bound on the nilpotency class (in fact, the nilpotency class must be strictly less than the order of matrices).