单李代数的抛物子代数上的线性交换映射

doi:10.13371/j.cnki.chin.q.j.m.2014.04.006

数学季刊 ›› 2014, Vol. 29 ›› Issue (4): 516-522.doi: 10.13371/j.cnki.chin.q.j.m.2014.04.006

单李代数的抛物子代数上的线性交换映射

School of Mathematics and Computer Science, Fujian Normal University

收稿日期:2012-12-25 出版日期:2014-12-30 发布日期:2020-11-26
作者简介:CHEN Zheng-xin(1976-), male, native of Qichun, Hubei, an associate professor of Fujian Normal University, Ph.D., engages in Representation theory of algebra.
基金资助:
Supported by the National Natural Science Foundation of China(11101084)； Supported by the Fujian Province Natural Science Foundation of China；

Linear Commuting Maps on Parabolic Subalgebras of Finite-dimensional Simple Lie Algebras

School of Mathematics and Computer Science, Fujian Normal University

Received:2012-12-25 Online:2014-12-30 Published:2020-11-26
About author:CHEN Zheng-xin(1976-), male, native of Qichun, Hubei, an associate professor of Fujian Normal University, Ph.D., engages in Representation theory of algebra.
Supported by:
Supported by the National Natural Science Foundation of China(11101084)； Supported by the Fujian Province Natural Science Foundation of China；

摘要/Abstract

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.

关键词: commuting maps, finite-dimensional simple Lie algebras, standard parabolic subalgebras

Abstract: 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.

Key words: commuting maps, finite-dimensional simple Lie algebras, standard parabolic subalgebras

中图分类号:

O152.5

陈正新, 汪冰. 单李代数的抛物子代数上的线性交换映射[J]. 数学季刊, 2014, 29(4): 516-522.

CHEN Zheng-xin, WANG Bing. Linear Commuting Maps on Parabolic Subalgebras of Finite-dimensional Simple Lie Algebras[J]. Chinese Quarterly Journal of Mathematics, 2014, 29(4): 516-522.

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单李代数的抛物子代数上的线性交换映射

Linear Commuting Maps on Parabolic Subalgebras of Finite-dimensional Simple Lie Algebras

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