Outer automorphism group of the ergodic equivalence relation generated by translations of dense subgroup of compact group on its homogeneous space

Sergey L. Gefter
1996 Publications of the Research Institute for Mathematical Sciences  
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\itR r using the D. Witte's rigidity theorem. Moreover, an example of an equivalence relation without outer automorphisms is constructed.
doi:10.2977/prims/1195162855 fatcat:unskl2wzvzehhf3kxabli4jigi