Derivations of locally simple Lie algebras

摘要

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.