On Nilpotent Groups of Algebra Automorphisms

The main purpose of this paper is to derive conclusions about the structure of a nilpotent group of algebra automorphisms and, in the case of a Lie algebra, about the influence of this nilpotence on the structure of the algebra. A motivation for this study is a well known theorem due to Kolchin: A unipotent linear group can be triangularized and is thus nilpotent. The converse is manifestly false, but we have (as an immediate consequence of Theorem 2.7)