交换环上D_n型Chevalley代数的由正根基向量生成的幂零子代数的自同构  

Automorphisms of the Nelpotent Subalgebra Generated by Positive Root Vectors of Chevalley Algebra of Type D_n Over Chmmunicative Ring

作　　者：蒋德志[1] 曹佑安[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2期10-20,共11页Natural Science Journal of Xiangtan University

基　　金：湖南省教育厅资助项目 (0 1A0 0 3 ) ;湖南省自然科学基金资助项目 (0 2JJY2 0 0 4)

摘　　要：设R是一个特征不是 2的整环或是一个以 2为单位的局部环 ,N是R上Dn(n≥ 4) 型Chevalley代数的由正根基向量生成的幂零子代数 .证明了N的任一个自同构 φ都可以唯一地表示为图自同构gσ 、对角自同构dχ 、极点自同构ξb 、中心自同构 μc 、内自同构i的乘积 ,并且N的自同构群Aut ,(N) =G | (D | ((E×C) | I) ) ,其中G ,D ,E ,C ,I分别是N的图自同构群、对角自同构群、极点自同构群、中心自同构群、内自同构群 .Let R be a local communicative ring that contains 2 as a unit or a communicative integral domain of characteristic other than 2.Let N be the nilpotent subalgebra generated by positive root vectors of chevalley algebra of type D_n(n≥4) over R. In this paper, we discuss the automorphism group of N. We prove that any automorphism φ of N can be uniquely expressed as φ=g_(σ)·d_(χ)·ξ_b·μ_c·i, where g_(σ), d_(χ), ξ_b,μ_c and i are graph, diagonal, extremal, central and inner automorphisms, respectively, of N and that the automorphism group Aut(N)=G｜(D｜((E×C)｜I)), where G,D,E,C and I are the graph, diagonal, extremal, central and inner automorphism groups, respectively, of N.

关 键 词：CHEVALLEY代数 处同构 幂零李代数 整环 局部环 

分 类 号：O152.5[理学—数学]