Outer Automorphism Group of the Ergodic Equivalence Relation Generated by Translations of Dense Subgroup of Compact Group on its Homogeneous Space | Zendy

S. L. Gefter | Zendy

Open Access

Outer Automorphism Group of the Ergodic Equivalence Relation Generated by Translations of Dense Subgroup of Compact Group on its Homogeneous Space

Author(s) -

S. L. Gefter

Publication year - 1996

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195162855

Subject(s) - mathematics , ergodic theory , homogeneous , outer automorphism group , group (periodic table) , automorphism , equivalence relation , homogeneous space , equivalence (formal languages) , locally compact space , pure mathematics , maximal subgroup , space (punctuation) , automorphism group , normal subgroup , combinatorics , geometry , physics , computer science , quantum mechanics , operating system

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.

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