单李代数的抛物子代数上的线性交换映射

陈正新, 汪冰

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

数学季刊 >

2014 , Vol. 29 >Issue 4: 516 - 522

DOI: https://doi.org/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

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School of Mathematics and Computer Science, Fujian Normal University

CHEN Zheng-xin(1976-), male, native of Qichun, Hubei, an associate professor of Fujian Normal University, Ph.D., engages in Representation theory of algebra.

收稿日期: 2012-12-25

网络出版日期: 2020-11-26

基金资助

Supported by the National Natural Science Foundation of China(11101084)； Supported by the Fujian Province Natural Science Foundation of China；

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

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School of Mathematics and Computer Science, Fujian Normal University

CHEN Zheng-xin(1976-), male, native of Qichun, Hubei, an associate professor of Fujian Normal University, Ph.D., engages in Representation theory of algebra.

Received date: 2012-12-25

Online published: 2020-11-26

Supported by

Supported by the National Natural Science Foundation of China(11101084)； Supported by the Fujian Province Natural Science Foundation of China；

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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

本文引用格式

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

Abstract

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

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