Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Isomorphism rigidity of commuting automorphisms


Author: Siddhartha Bhattacharya
Journal: Trans. Amer. Math. Soc. 360 (2008), 6319-6329
MSC (2000): Primary 37A35, 37A15
Published electronically: July 24, 2008
MathSciNet review: 2434289
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 37A35, 37A15

Retrieve articles in all journals with MSC (2000): 37A35, 37A15


Additional Information

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

DOI: http://dx.doi.org/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
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.