一类非简约李代数的饱和秩  

Saturation Rank for a Classof Non-reductive Lie Algebras

作　　者：潘阳 叶昌 PAN Yang;YE Chang(School of Artificial Intelligence and Big Data,Hefei University,Hefei 230601,China;School of Science,Huzhou University,Huzhou 313000,China)

机构地区：[1]合肥学院人工智能与大数据学院,安徽合肥230601 [2]湖州师范学院理学院,浙江湖州313000

出　　处：《湖州师范学院学报》2021年第2期14-20,共7页Journal of Huzhou University

基　　金：National Natural Science Foundation of China(11901195);University Natural Science Research Project of Anhui Province(KJ2019A0845);Scientific Research Foundation of Hefei University(18-19RC57);Scientific Research Project of Huzhou University(2018XJKJ48)。

摘　　要：研究特征为素数p的代数闭域上一类非简约李代数的饱和秩.更确切地,如果p_(J)是sl_(n+1)的标准抛物子代数,u_J是其对应的幂零根基,则揭示当|J∣=1且p≥n+1时,u_(J)的饱和秩等于代数k-群SL_(n+1)(k)的半单秩.In this article,we investigate the saturation rank of a class of non-reductive Lie algebras,defined over an algebraically closed field k of positive characteristic p.More precisely,if p J is a standard parabolic subalgebra of sl n+1 and u J is the corresponding nilradical,we show that the saturation rank of u J equals the semisimple rank of the algebraic k-group SL n+1(k)when J=1 and p≥n+1.

关 键 词：饱和秩 抛物子代数 Richardson元 

分 类 号：O152.5[理学—数学]