Transactions of the American Mathematical Society

Author(s): Siddhartha Bhattacharya
Journal: Trans. Amer. Math. Soc. 360 (2008), 6319-6329.
MSC (2000): Primary 37A35, 37A15
Posted: July 24, 2008
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Abstract: Let

, and let $(X,\alpha)$ and $(Y,\beta)$ be two zero-entropy ${\mathbb{Z}}^d$ -actions on compact abelian groups by

commuting automorphisms. We show that if all lower rank subactions of $\alpha$ and $\beta$ have completely positive entropy, then any measurable equivariant map from

is an affine map. In particular, two such actions are measurably conjugate if and only if they are algebraically conjugate.

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Siddhartha Bhattacharya
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Mumbai 400005, India
Email: siddhart@math.tifr.res.in

DOI: 10.1090/S0002-9947-08-04597-2
PII: S 0002-9947(08)04597-2
Keywords: Rigidity, commuting automorphisms, entropy
Received by editor(s): November 6, 2006
Posted: July 24, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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