On the derivation algebras of Lie module triple systems

Abstract

We continue here work on the classification of Lie module triple systems over an algebraically closed field k of characteristic zero begun in [4], where we indicated how to decompose a Lie module triple system under certain restrictions into constituents from two relatively simple subclasses. We study these two subclasses in the present paper. Recall [S] that a Lie module triple system (abbreviated LMTS) is formed from a finite dimensional Lie algebra 27 having a nondegenerate symmetric associative (invariant) bilinear form b and a finite dimensional faithful Y-module M having a nondegenerate Y-invariant bilinear form cp, that is,