Non-linear Maps on Borel Subalgebras of Simple Lie Algebras Preserving Abelin Ideals  

单李代数的Borel子代数的保可换理想的非线性映射(英文)

作　　者：赵延霞 王登银 

机构地区：[1]School of Mathematics and Information Science,Henan Polytechnic University [2]Department of Mathematics,China University of Mining and Technology

出　　处：《Chinese Quarterly Journal of Mathematics》2012年第4期615-623,共9页数学季刊（英文版）

基　　金：Supported by the Doctor Foundation of Henan Polytechnic University(B2010-93);Supported by the National Natural Science Foundation of China(11126121);Supported by the Natural Science Foundation of Henan Province(112300410120);Supported by the Natural Science Research Program of Education Department of Henan Province(201lB110016);Supported by the Applied Mathematics Provincial-level Key Discipline of Henan Province of Henau Polytechuic University

摘　　要：Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In this article, by using some results of Chevalley groups, the theory of root systems and root space decomposition, the author gives an explicit description on such maps of Ь.

关 键 词：simple Lie algebra abelian ideal non-linear map 

分 类 号：O151.2[理学—数学]