Journal of Lie Theory

no. 2
Derivations of Locally Simple Lie Algebras
Journal of Lie Theory, Volume 15 (2005) no. 2, pp. 589-594
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.
DOI: 10.5802/jolt.392
Classification: 17B65, 17B20, 17B56
Keywords: Locally finite Lie algebra, simple Lie algebra, derivation, direct limit 
@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},
     doi = {10.5802/jolt.392},
     zbl = {1064.17013},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.392/}
}
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K.-H. Neeb. Derivations of Locally Simple Lie Algebras. Journal of Lie Theory, Volume 15 (2005) no. 2, pp. 589-594. doi: 10.5802/jolt.392

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