Journal of Lie Theory

no. 1
On Derivations of Parabolic Lie Algebras
Journal of Lie Theory, Volume 27 (2017) no. 1, pp. 217-236
Let g be a reductive Lie algebra over an algebraically closed, characteristic zero field or over the reals R. Let q be a parabolic subalgebra of g. We characterize the derivations of q by decomposing the derivation algebra as the direct sum of two ideals: one of which is the image of the adjoint representation and the other consists of all linear transformations on q that map q into its center and map the derived algebra of q to 0.
DOI: 10.5802/jolt.942
Classification: 16W25, 17B45
Keywords: Derivation, parabolic subalgebra, reductive Lie algebra 
@article{JOLT_2017_27_1_a11,
     author = {D. Brice},
     title = {On {Derivations} of {Parabolic} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {217--236},
     year = {2017},
     volume = {27},
     number = {1},
     doi = {10.5802/jolt.942},
     zbl = {1386.17012},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.942/}
}
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D. Brice. On Derivations of Parabolic Lie Algebras. Journal of Lie Theory, Volume 27 (2017) no. 1, pp. 217-236. doi: 10.5802/jolt.942

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