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Journal of Lie Theory 27 (2017), No. 1, 217--236
Copyright Heldermann Verlag 2017

On Derivations of Parabolic Lie Algebras

Daniel Brice
Dept. of Mathematics, California State University, 9001 Stockdale Highway, Bakersfield, CA 93311, U.S.A.

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.

Keywords: Derivation, parabolic subalgebra, reductive Lie algebra.

MSC: 16W25, 17B45

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