Journal of Lie Theory

no. 1
Product Zero Derivations of the Parabolic Subalgebras of Simple Lie Algebras
Dengyin Wang1; Wei Zhang1; Zhengxin Chen2
1Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, P. R. China
2School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, P. R. China
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

Dengyin Wang  1 ; Wei Zhang  1 ; Zhengxin Chen  2

1 Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, P. R. China
2 School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, P. R. China 
Dengyin Wang; Wei Zhang; Zhengxin 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
@article{JOLT_2010_20_1_a9,
     author = {Dengyin Wang and Wei Zhang and Zhengxin 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  - Dengyin Wang
AU  - Wei Zhang
AU  - Zhengxin 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 Dengyin Wang
%A Wei Zhang
%A Zhengxin 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

Cited by Sources: