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On Constructing Ergodic Hyperfinite Equivalence Relations of Non-Product Type |
Canad. Math. Bull. 56(2013), 136-147
Published:2011-06-29
Printed: Mar 2013
Printed: Mar 2013
- Radu-Bogdan Munteanu,
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 |
| MSC Classifications: |
37A20 - Orbit equivalence, cocycles, ergodic equivalence relations 37A35 - Entropy and other invariants, isomorphism, classification 46L10 - General theory of von Neumann algebras |