
arXiv: 1504.08286
Let $\mathfrak{g}$ be a reductive Lie algebra over an algebraically closed, characteristic zero field or over $\mathbb{R}$. Let $\mathfrak{q}$ be a parabolic subalgebra of $\mathfrak{g}$. We characterize the derivations of $\mathfrak{q}$ by decomposing the derivation algebra as the direct sum of two ideals: one of which being the image of the adjoint representation and the other consisting of all linear transformations on $\mathfrak{q}$ that map into the center of $\mathfrak{q}$ and map the derived algebra of $\mathfrak{q}$ to $0$.
parabolic subalgebra, 16W25, 17B45, Lie algebras of linear algebraic groups, Rings and Algebras (math.RA), Automorphisms, derivations, other operators for Lie algebras and super algebras, reductive Lie algebra, FOS: Mathematics, derivation, Mathematics - Rings and Algebras, Derivations, actions of Lie algebras, Simple, semisimple, reductive (super)algebras
parabolic subalgebra, 16W25, 17B45, Lie algebras of linear algebraic groups, Rings and Algebras (math.RA), Automorphisms, derivations, other operators for Lie algebras and super algebras, reductive Lie algebra, FOS: Mathematics, derivation, Mathematics - Rings and Algebras, Derivations, actions of Lie algebras, Simple, semisimple, reductive (super)algebras
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