Λ-稳定秩下的酉K_1-群  

UNITARY K_1-GROUPS UNDER A-STABLE RANGE CONDITION

作　　者：唐国平[1] 

机构地区：[1]中国科学院研究生院数学系

出　　处：《数学年刊（A辑）》2004年第2期171-178,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10271094);科学院百人计划资助的项目.

摘　　要：A.Bak和唐国平在[1]中引入了Λ-稳定秩条件,这是比过去常用的酉稳定秩条件与绝对稳定秩条件都要弱的新的稳定秩条件.利用这一稳定秩条件证明了酉群(有限生成投射模上二次型的自同构群)的基本子群的正规性、二次型空间的消去性.以及酉K1-群的稳定性.这些结果不仅推广了已有的类似结果、极大地简化了证明过程,而更重要的是降低了稳定秩的下界.In this paper, by using A-stable range condition, which was introduced by A. Bak and G. Tang [1] and weaker than both unitary stable range condition and absolute stable range condition, the author proves that the normality of elementary subgroup of unitary groups (group of automorphisms of non-singular quadratic spaces over finitely generated modules), cancellation property for quadratic spaces, and the stability of unitary K1-groups. The proofs are not only easier than the existing similar results, but also give better lower boundaries on the rank of unitary groups.

关 键 词：酉群 ∧-稳定秩条件 正规性 酉K1-群的稳定性 

分 类 号：O152[理学—数学]