Geodesic
Product Zero Derivations of the Parabolic Subalgebras of Simple Lie Algebras
Journal of Lie theory, Tome 20 (2010) no. 1, pp. 167-174.

Voir la notice de l'article provenant de la source Heldermann Verlag

\def\b{{\frak b}} \def\g{{\frak g}} \def\p{{\frak p}} Let $\g$ be a simple Lie algebra of rank $l$ over an algebraic closed field of characteristic zero, $\b$ a Borel subalgebra of $\g$, $\p$ a parabolic subalgebra of $\g$ containing $\b$. A linear map $\varphi$ on $\p$ is called a product zero derivation if, for $x, y\in \p$, $[x,y]=0$ implies $[\varphi(x), y]+[x,\varphi(y)]=0$. It is shown in this paper that a product zero derivation $\varphi$ on $\p$ is just a sum of an inner derivation and a scalar multiplication map in case that $l\geq 2$.
Classification : 17B20, 17B30, 17B40
Mots-clés : Simple Lie algebras, parabolic subalgebras, derivations of Lie algebras 
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     title = {Product {Zero} {Derivations} of the {Parabolic} {Subalgebras} of {Simple} {Lie} {Algebras}},
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D. Wang; W. Zhang; Z. Chen . Product Zero Derivations of the Parabolic Subalgebras of Simple Lie Algebras. Journal of Lie theory, Tome 20 (2010) no. 1, pp. 167-174. http://geodesic.mathdoc.fr/item/JLT_2010_20_1_JLT_2010_20_1_a9/