On subrelations of ergodic measured type III equivalence relations

Alexandre Danilenko

Colloquium Mathematicae (2000)

  • Volume: 84/85, Issue: 1, page 13-22
  • ISSN: 0010-1354

Abstract

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We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.

How to cite

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Danilenko, Alexandre. "On subrelations of ergodic measured type III equivalence relations." Colloquium Mathematicae 84/85.1 (2000): 13-22. <http://eudml.org/doc/210792>.

@article{Danilenko2000,
abstract = {We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.},
author = {Danilenko, Alexandre},
journal = {Colloquium Mathematicae},
keywords = {orbit theory; ergodic relations},
language = {eng},
number = {1},
pages = {13-22},
title = {On subrelations of ergodic measured type III equivalence relations},
url = {http://eudml.org/doc/210792},
volume = {84/85},
year = {2000},
}

TY - JOUR
AU - Danilenko, Alexandre
TI - On subrelations of ergodic measured type III equivalence relations
JO - Colloquium Mathematicae
PY - 2000
VL - 84/85
IS - 1
SP - 13
EP - 22
AB - We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.
LA - eng
KW - orbit theory; ergodic relations
UR - http://eudml.org/doc/210792
ER -

References

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  8. [GS2] V. Ya. Golodets and S. D. Sinel'shchikov, Classification and structure of cocycles of amenable ergodic equivalence relations, J. Funct. Anal. 121 (1994), 455-485. Zbl0821.28010
  9. [Ha] T. Hamachi, Suborbits and group extensions of flows, Israel J. Math. 100 (1997), 249-283. Zbl0880.46046
  10. [HO] T. Hamachi and M. Osikawa, Ergodic groups of automorphisms and Krieger's theorems, Sem. Math. Sci. Keio Univ. 3 (1981). Zbl0472.28015
  11. [Kr] W. Krieger, On ergodic flows and isomorphism of factors, Math. Ann. 223 (1976), 19-70. Zbl0332.46045
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  13. [Zi] R. Zimmer, Extensions of ergodic group actions, Illinois J. Math. 20 (1976), 373-409. Zbl0334.28015

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