Derivations of Locally Simple Lie Algebras

Let g be a locally finite Lie algebra over a field of characteristic zero which is a direct limit of finite-dimensional simple ones.In this short note it is shown that each invariant symmetric bilinear form on g is invariant under all derivations and that each such form defines a natural embedding der g g * .The latter embedding is used to determine der g explicitly for all locally finite split simple Lie algebras.

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