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arXiv · 1504.08286

On derivations of parabolic Lie algebras

Daniel Brice
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Abstract

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 $0$.

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Daniel Brice. 2015-04-30. On derivations of parabolic Lie algebras. https://arxiv.org/abs/1504.08286

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