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.
出处
《湘潭大学自然科学学报》
CAS
CSCD
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)
