Linear Groups Definable in o-Minimal Structures☆
Linear Groups Definable in o-Minimal Structures☆
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o-最小结构中可定义的线性群☆
DOI：
10.1006/jabr.2001.8861
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发表时间：
2002
影响因子：
0.9
通讯作者：
S. Starchenko
中科院分区：
文献类型：
--
作者：
Y. Peterzil;A. Pillay;S. Starchenko
研究了GL（n，R）的子群G可定义在真实的闭域R的o-极小扩张M =（R，+，·，.）中.我们证明了几个结果，如：（a）G可以定义使用的字段结构在R上，如果必要的话，幂函数，或指数函数定义在M。(b)若G没有无穷正规可定义的阿贝尔子群，则G是半代数的。我们还刻画了可定义在o-极小结构中的可定义单群为与单李群初等等价的群，并证明了真实的闭域上的Kneser-Tits猜想.
We study subgroups G of GL(n, R) definable in o-minimal expansions M = (R, +, · ,…) of a real closed field R. We prove several results such as: (a) G can be defined using just the field structure on R together with, if necessary, power functions, or an exponential function definable in M. (b) If G has no infinite, normal, definable abelian subgroup, then G is semialgebraic. We also characterize the definably simple groups definable in o-minimal structures as those groups elementarily equivalent to simple Lie groups, and we give a proof of the Kneser–Tits conjecture for real closed fields.