Journal of Lie Theory

no. 1
Product Zero Derivations of the Parabolic Subalgebras of Simple Lie Algebras
Journal of Lie Theory, Volume 20 (2010) no. 1, pp. 167-174
\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 $l\geq 2$.
DOI: 10.5802/jolt.591
Classification: 17B20, 17B30, 17B40
Keywords: Simple Lie algebras, parabolic subalgebras, derivations of Lie algebras 
@article{JOLT_2010_20_1_a9,
     author = {D. Wang and W. Zhang and Z. Chen},
     title = {Product {Zero} {Derivations} of the {Parabolic} {Subalgebras} of {Simple} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {167--174},
     year = {2010},
     volume = {20},
     number = {1},
     doi = {10.5802/jolt.591},
     zbl = {1228.17013},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.591/}
}
TY  - JOUR
AU  - D. Wang
AU  - W. Zhang
AU  - Z. Chen
TI  - Product Zero Derivations of the Parabolic Subalgebras of Simple Lie Algebras
JO  - Journal of Lie Theory
PY  - 2010
SP  - 167
EP  - 174
VL  - 20
IS  - 1
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.591/
DO  - 10.5802/jolt.591
ID  - JOLT_2010_20_1_a9
ER  - 
%0 Journal Article
%A D. Wang
%A W. Zhang
%A Z. Chen
%T Product Zero Derivations of the Parabolic Subalgebras of Simple Lie Algebras
%J Journal of Lie Theory
%D 2010
%P 167-174
%V 20
%N 1
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.591/
%R 10.5802/jolt.591
%F JOLT_2010_20_1_a9
D. Wang; W. Zhang; Z. Chen. Product Zero Derivations of the Parabolic Subalgebras of Simple Lie Algebras. Journal of Lie Theory, Volume 20 (2010) no. 1, pp. 167-174. doi: 10.5802/jolt.591

Cited by Sources: