On Derivations and Holomorphs of Nilpotent Lie Algebras

Abstract

A linear Lie algebra is called toroidal if it is abelian and consists of semi-simple transformations. The maximum, t(L), of the dimensions of the toroidal subalgebras of the derivation algebra, Δ(L), is an invariant of L. This paper is mainly concerned with the relation between the magnitude of t(L) for nilpotent L and the structures of L and Δ(L).