Abstract
We explore the role derivations of a Lie triple system 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 and the semisimplicity of T are also studied.
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