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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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