Outer automorphism group of the ergodic equivalence relation generated by translations of dense subgroup of compact group on its homogeneous space
Outer automorphism group of the ergodic equivalence relation generated by translations of dense subgroup of compact group on its homogeneous space
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紧群稠密子群在齐次空间上平移生成的遍历等价关系的外自同构群
DOI：
10.2977/prims/1195162855
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发表时间：
1996
影响因子：
1.2
通讯作者：
S. Gefter
中科院分区：
文献类型：
--
作者：
S. Gefter
本文研究了紧致群K上半单李群中格F的作用所生成的遍历等价关系Rr的外自同构群OutRr。证明了OutRr是局部紧的.如果K是连通单李群，我们利用D.维特刚性定理。此外，构造了一个没有外自同构的等价关系的例子。
We study the outer automorphism group OutRr of the ergodic equivalence relation Rr generated by the action of a lattice F in a semisimple Lie group on the homogeneos space of a compact group K. It is shown that OutRr is locally compact. If K is a connected simple Lie group, we prove the compactness of 0\itRr using the D. Witte's rigidity theorem. Moreover, an example of an equivalence relation without outer automorphisms is constructed.