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Minimal self-joinings for nonsingular transformations

Published online by Cambridge University Press:  19 September 2008

Daniel J. Rudolph  and
Cesar E. Silva
Daniel J. Rudolph
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
Cesar E. Silva
Affiliation:
Department of Mathematics, Williams College, Williamstown, Massachusetts, 01267, USA
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Abstract

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The notion of minimal self-joinings for conservative nonsingular actions is defined as a restriction on the nature of rational self-joinings. The need to consider rational joinings is demonstrated by showing that any two type II1 actions whose Cartesian product is ergodic have type IIIλ nonsingular joinings. Lastly, actions of all Krieger types with minimal self-joinings are constructed. Hence these actions are prime and commute only with their powers.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 4 , December 1989 , pp. 759 - 800
Copyright
Copyright © Cambridge University Press 1989

References

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