
Journal of Lie Theory 15 (2005), No. 2, 589594 Copyright Heldermann Verlag 2005 Derivations of Locally Simple Lie Algebras KarlHermann Neeb Fachbereich Mathematik, Technische Universitaet, Schlossgartenstrasse 7, 64289 Darmstadt, Germany neeb@mathematik.tudarmstadt.de Let g be a locally finite Lie algebra over a field of characteristic zero which is a direct limit of finitedimensional 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 [ Fulltextpdf (139 KB)] for subscribers only. 