既约么半群M_n(K)(英文)  

On Reductive Monoid M_n(K)

作　　者：曹佑安[1] 李卓[1] 

机构地区：[1]湘潭大学数学系,湖南湘潭411105

出　　处：《湘潭大学自然科学学报》2004年第1期140-147,共8页Natural Science Journal of Xiangtan University

基　　金：ProjectsupportedbyHunanProvincialNaturalScienceFoundationofChina(No .0 2JJY2 0 0 4)andScienceandResearchFundofHunanProvincialEducationDepartment (No .0 1A0 0 3 )

摘　　要：　主要介绍Renner得到的重要结果代数么半群的Bruhat分解 这一结果是Putcha-Renner理论系统发展的一个里程碑 当保留首先被Renner发现时,它甚至对Mn(K)也是新的 该文利用线性代数知识对Mn(K)的Bruhat分解给出一个初等描述,并且给出所有秩2,半单秩1的既约么半群 作者用初等方法证明了Mn(K)的Bruhat分解。This article serves as an introduction to one of the amazing results established by Renner which is the analogue of the Bruhat decomposition of algebraic monoids. This result is a milestone in the system development of PutchaRenner theory. It was even new to M_n(K) when it was first found by Renner. In this article we give an elementary description to M_n(K) using linear algebra knowledge and list all rank two, semisimple rank one reductive monoids. We prove the analogue of Bruhat decomposition for M_n(K) in an elementary way. Finally we pose some open problems on Hecke algebras related to Renner monoids.

关 键 词：代数群 代数么半群 Bruhat分解 HECKE代数 

分 类 号：O152.7[理学—数学]