摘要
A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.
A map φ on a Lie algebra g is called to be commuting if [φ（x）,x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear map φ on P is commuting if and only if φ is a scalar multiplication map on P.
基金
Supported by the National Natural Science Foundation of China（Ill01084）
Supported by the Fujian Province Natural Science Foundation of China
