Unipotent Group

A unipotent algebraic group over a characteristic-zero field is an algebraic group admitting a faithful finite-dimensional representation in which every element is a unipotent matrix. Such a matrix has all eigenvalues equal to 1 over the algebraic closure. The additive group and the group of upper triangular matrices with all diagonal entries 1 are examples. An inverse limit of unipotent algebraic groups is called pro-unipotent. Unipotent completion retains the group representations that take values in such groups. In characteristic zero these groups are nilpotent, but the nilpotency class can grow with dimension.