D_4^(3)型仿射 Chevalley代数的理想  

Ideals in the Affine Chevalley Algebra of Type D_4~

作　　者：刘昌堃[1] 

机构地区：[1]同济大学数学系

出　　处：《同济大学学报（自然科学版）》1989年第3期369-376,共8页Journal of Tongji University:Natural Science

摘　　要：设R是具有恒等元的可换环,J.F.Hurley在1969年与1981年分别对有限维复单李代数及k=1的仿射李代数L研究了相应的Chevalley代数L_R=RL_z的理想结构。本文用D.Mitzman获得的对k=2,3型仿射李代数之Chevalley基,推广Hurley的结果,给出了R上D_4^((3))型仿射Chevalley代数L_R的理想结构。用正合列C→RC_0→L_R→L_R→0,它归结为loop代数L_R=L(g,σ)R的理想结构,我们得到: 设2,3不是R中的零因子,P=R[t^3;t^(-3)]并记L_p=L_R,则对L_p的任一非零理想I,必存在P中理想J,使得6JL_pIJL_p,特别当R是特征零的域时,则I=JL_P(该结果与Kac在1983年得到的结果一致)。Chevalley algebras L_R = R.L_Z associated with finite-dimensional simpleLie algebras and affine Lie algebras of type k =1 over a commutative ring withidentity were defined by J. Hurley in 1969 and 1981 respectively, and theirideal structures were worked out there. The goal of this paper is to extend Hurley' s result to the affine Cheva-lley algebra L_R of type D by using Mitzman' s Chevalley basis. The idealstructure of L_R can be reduced to the ideal structure of its loop algebra L_R= L(g, a)_ R by the exact sequence 0 →R_(c_o)→L_R→L_R→0, and weobtain: Assume that 2,3 are not zero divisors in R, P = R[t^3, t-3] and I is anideal of L_R. Then there exists an ideal JP such that 6JL_RIJL_R. In parti-cular, if R = K, a field of characteristic zero, then I =JL_R. (This result coin-cides with Kac, 1983 )

关 键 词：仿射 李代数 理想 可换环 LOOP代数 

分 类 号：O152.5[理学—数学]