Geodesic
Derivations of Locally Simple Lie Algebras
Journal of Lie Theory, Tome 15 (2005) no. 2, pp. 589-594

Voir la notice de l'article provenant de la source Heldermann Verlag

Zbl   EuDML

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 
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/JOLT_2005_15_2_a12/
@article{JOLT_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},
     zbl = {1064.17013},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2005_15_2_a12/}
}
TY  - JOUR
AU  - K.-H. Neeb
TI  - Derivations of Locally Simple Lie Algebras
JO  - Journal of Lie Theory
PY  - 2005
SP  - 589
EP  - 594
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JOLT_2005_15_2_a12/
ID  - JOLT_2005_15_2_a12
ER  - 
%0 Journal Article
%A K.-H. Neeb
%T Derivations of Locally Simple Lie Algebras
%J Journal of Lie Theory
%D 2005
%P 589-594
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2005_15_2_a12/
%F JOLT_2005_15_2_a12