Geodesic
Derivations of Locally Simple Lie Algebras
Journal of Lie theory, Tome 15 (2005) no. 2, pp. 589-594 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 17B65, 17B20, 17B56
Mots-clés : Locally finite Lie algebra, simple Lie algebra, derivation, direct limit 
@article{JLT_2005_15_2_JLT_2005_15_2_a12,
     author = {K.-H. Neeb },
     title = {Derivations of {Locally} {Simple} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {589--594},
     year = {2005},
     volume = {15},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2005_15_2_JLT_2005_15_2_a12/}
}
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K.-H. Neeb . Derivations of Locally Simple Lie Algebras. Journal of Lie theory, Tome 15 (2005) no. 2, pp. 589-594. http://geodesic.mathdoc.fr/item/JLT_2005_15_2_JLT_2005_15_2_a12/