交换环上由B_n型Chevalley代数的正根基向量生成的幂零子代数的自同构  

Automorphisms of the Nilpotent Subalgebras Generated by the Positive Root Vectors of Chevalley Algebras of Type B_n Over Commutative Rings

作　　者：王军英[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3期1-11,共11页Natural Science Journal of Xiangtan University

基　　金：国家自然科学基金资助科研项目(1047116);湖南省自然科学基金资助科研项目(02JJY2004);湖南省教育厅资助科研项目(01A003)

摘　　要：　设R是一个以2为单位的交换环,N是R上由Bn型Chevalley代数的正根基向量生成的幂零子代数.证明了N(n≥4)的任一个自同构φ都可以唯一地表示为对角自同构dχ、极点自同构ξb、中心自同构μc、内自同构σ的乘积,并且N的自同构群Aut(N)=D｜ ((E×C)｜ I),其中D,E,C,I分别是N(n≥4)的对角自同构群、极点自同构群、中心自同构群、内自同构群.对于n=2,3的情况,我们也确定了N的自同构.Let R be a communicative ring that contains 2 as a unit.Let N be the nilpotent subalgebra generated by positive root vectors of chevalley algebra of type B_n over R.In this paper,we determine the automorphism group of N(n≥4). We prove that any automorphism φ of N can be uniquely expressed as φ=d_(χ)·ξ_b·μ_c·i, where d_(χ),ξ_b,μ_c and σ are diagonal, extremal, central and inner automorphisms, respectively, of N and that the automorphism group Aut(N)=D｜((E×C)｜I), where D,E,C and I are the diagonal, extremal, central and inner automorphism groups, respectively, of N. For the case of n=2, 3, we also determine the automorphism group of N.

关 键 词：CHEVALLEY代数 自同构 幂零李代数 交换环 

分 类 号：O152.5[理学—数学]