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Journal of Lie Theory 15 (2005), No. 2, 589--594
Copyright Heldermann Verlag 2005

Derivations of Locally Simple Lie Algebras

Karl-Hermann Neeb
Fachbereich Mathematik, Technische Universitaet, Schlossgartenstrasse 7, 64289 Darmstadt, Germany

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 from g into g*. The latter embedding is used to determine der(g) explicitly for all locally finite split simple Lie algebras.

Keywords: Locally finite Lie algebra, simple Lie algebra, derivation, direct limit.

MSC: 17B65, 17B20, 17B56

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