幂零李群的Malcev基坐标变换研究  

Study on Nilpotent Lie Group’s Malcev Coordinate Transformation

作　　者：许芳 XU Fang(Hefei College of Economics,Hefei 230031,China)

机构地区：[1]合肥经济学院基础课教学部,合肥230031

出　　处：《湖南工程学院学报(自然科学版)》2024年第3期57-62,79,共7页Journal of Hunan Institute of Engineering(Natural Science Edition)

基　　金：安徽省自然科学研究项目(KJ2020A1176)

摘　　要：设G是一个m维幂零李群,g为G的关联李代数,exp:g→G是指数映射.设g的一组Malcev基为{X_(1),X_(2),…,X_(m)},由Campbell-Baker-Hausdorff公式可知,exp(t_(1)X_(1))…exp(t_(m)X_(m))=exp(^(m)∑_(i=1)P_(i)(t)X_(i)).我们利用Malcev基坐标的性质,计算出基变换多项式P_(i)(t)具体的表达式,并指出什么样的多项式可以是Malcev基变换多项式.Let G be a nilpotent Lie group of dimension m,g a Lie Algebra associated with G,and exp:g→G an exponential mapping.Let{X_(1),X_(2),⋯,X_(m)}be a set of bases of g,and according to the Campbell-Baker-Hausdorff formula,we know exp(t_(1)X_(1))exp(t_(2)X_(2))⋯exp(t_(m)X_(m))=exp(^(m)∑_(i=1)P_(i)(t)X_(i)).We use the properties of the Malcev base coordinates to calculate the specific expression of the base transformation polynomial and indicate what kind of polynomial is the Malcev basis transformation polynomia.

关 键 词：幂零李群 Malcev基 基坐标变换 

分 类 号：O152.5[理学—数学]