
Journal of Lie Theory 27 (2017), No. 1, 217236 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. dbrice@cj.com 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 [ Fulltextpdf (397 KB)] for subscribers only. 