The role of derivations in the nilpotence and semi-simplicity of Lie triple systems

Abstract

We explore the role derivations of a Lie triple system T play in the nilpotence and semisimplicity of T. In particular analogous to two theorems of Jacobson for Lie algebras, (by giving a sufficient condition for the nilpotence of T in terms of the existence of an invertible derivation, and in terms of the existence of certain automorphisms), are stated. The connections between the Lie algebra of derivations of T and the semisimplicity of T are also studied.