## Isomorphism rigidity of commuting automorphisms

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- by Siddhartha Bhattacharya PDF
- Trans. Amer. Math. Soc.
**360**(2008), 6319-6329 Request permission

## 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.## References

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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
- Received by editor(s): November 6, 2006
- Published electronically: July 24, 2008
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2434289