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On Constructing Ergodic Hyperfinite Equivalence Relations of Non-Product Type

  Published:2011-06-29
 Printed: Mar 2013
  • Radu-Bogdan Munteanu,
    University of Bucharest, Faculty of Chemistry, Department of Physics and Applied Mathematics, 4-12 Bd. Regina Elisabeta, 030018, Sector 1, Bucharest, Romania
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Abstract

Product type equivalence relations are hyperfinite measured equivalence relations, which, up to orbit equivalence, are generated by product type odometer actions. We give a concrete example of a hyperfinite equivalence relation of non-product type, which is the tail equivalence on a Bratteli diagram. In order to show that the equivalence relation constructed is not of product type we will use a criterion called property A. This property, introduced by Krieger for non-singular transformations, is defined directly for hyperfinite equivalence relations in this paper.
Keywords: property A, hyperfinite equivalence relation, non-product type property A, hyperfinite equivalence relation, non-product type
MSC Classifications: 37A20, 37A35, 46L10 show english descriptions Orbit equivalence, cocycles, ergodic equivalence relations
Entropy and other invariants, isomorphism, classification
General theory of von Neumann algebras
37A20 - Orbit equivalence, cocycles, ergodic equivalence relations
37A35 - Entropy and other invariants, isomorphism, classification
46L10 - General theory of von Neumann algebras
 

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