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Some remarks on the entropy for algebraic actions of amenable groups


Authors: Nhan-Phu Chung and Andreas Thom
Journal: Trans. Amer. Math. Soc. 367 (2015), 8579-8595
MSC (2010): Primary 37B40
DOI: https://doi.org/10.1090/S0002-9947-2014-06348-4
Published electronically: November 12, 2014
MathSciNet review: 3403066
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Abstract: In this short note we study the entropy for algebraic actions of certain amenable groups. The possible values for this entropy are studied. Various fundamental results about certain classes of amenable groups are re-proved using elementary arguments and the entropy invariant. We provide a natural decomposition of the entropy into summands contributed by individual primes and a summand corresponding to $ \infty $. These results extend previous work by Lind and Ward on $ p$-adic entropy.


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Additional Information

Nhan-Phu Chung
Affiliation: Max Planck Institute for Math in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
Address at time of publication: Department of Mathematics, University of Sciences, Vietnam National University at Ho Chi Minh City, 227 Nguyen Van Cu, P4, Q5, TP.HCM, Vietnam
Email: chung@mis.mpg.de, cnphu@hcmus.edu.vn

Andreas Thom
Affiliation: Mathematisches Institut, University of Leipzig, PF 100920, 04009 Leipzig, Germany
Address at time of publication: Technische Universität Dresden, 01062 Dresden, Germany
Email: andreas.thom@math.uni-leipzig.de, andreas.thom@tu-dresden.de

DOI: https://doi.org/10.1090/S0002-9947-2014-06348-4
Received by editor(s): March 15, 2013
Received by editor(s) in revised form: October 16, 2013
Published electronically: November 12, 2014
Article copyright: © Copyright 2014 American Mathematical Society