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单位上三角矩阵群的注记(Ⅲ)
引用本文:刘合国,吴佐慧.单位上三角矩阵群的注记(Ⅲ)[J].数学学报,2012(5):769-780.
作者姓名:刘合国  吴佐慧
作者单位:湖北大学数学系;广西柳州高级中学
基金项目:国家自然科学基金资助项目(10971054)
摘    要:设k_(ij)(1≤ij≤n)是给定的正整数,分别记G={ (1 k12a12…k1na1n 0 1…k2na2n…… 0 0…1 )|aij∈Z},R={ (0 k12a12…k1na1n……0 0…k2na2n 0 0…1 )|aij∈Z},本文证明:当G成群且G的上、下中心群列重合时,其相伴Lie环L(G)与Lie环R同构,其中R的Lie积定义为A,B]=AB-BA.即得到了此时L(G)的矩阵表示.

关 键 词:Lie环  相伴Lie环  单位上三角矩阵群

On the Unitriangular Group over the Integral Ring(Ⅲ)
He Guo LIU.On the Unitriangular Group over the Integral Ring(Ⅲ)[J].Acta Mathematica Sinica,2012(5):769-780.
Authors:He Guo LIU
Institution:Liuzhou Senior High School,Liuzhou 545006,P.R.China
Abstract:Let Tr1(n,Z) be the group of all n x n(upper) unitriangular matrices over the integral ring.Let kij(1≤i≤j≤n) be given positive integers and G={ (1 k12a12…k1na1n 0 1…k2na2n…… 0 0…1 )|aij∈Z},R={ (0 k12a12…k1na1n……0 0…k2na2n 0 0…1 )|aij∈Z}, If G is a subgroup of Tr1(n,Z),an d its upper central series coincides with its lower central series,then the associated Lie ring L(G) of G is isomorphic to the Lie ring R,where the Lie product of A,B is defined asA,B]= AB - BA for arbitrary two elements A and B of R.That is to say,we obtain the matrix representation of L(G).
Keywords:Lie ring  associated Lie ring  unitriangular group
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