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Isomorphism rigidity of commuting automorphisms


Author: Siddhartha Bhattacharya
Journal: Trans. Amer. Math. Soc. 360 (2008), 6319-6329
MSC (2000): Primary 37A35, 37A15
DOI: https://doi.org/10.1090/S0002-9947-08-04597-2
Published electronically: July 24, 2008
MathSciNet review: 2434289
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Abstract: Let $ d > 1$, and let $ (X,\alpha)$ and $ (Y,\beta)$ be two zero-entropy $ {\mathbb{Z}}^d$-actions on compact abelian groups by $ d$ commuting automorphisms. We show that if all lower rank subactions of $ \alpha$ and $ \beta$ have completely positive entropy, then any measurable equivariant map from $ X$ to $ Y$ is an affine map. In particular, two such actions are measurably conjugate if and only if they are algebraically conjugate.


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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9947-08-04597-2
Keywords: Rigidity, commuting automorphisms, entropy
Received by editor(s): November 6, 2006
Published electronically: July 24, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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