Some remarks on the entropy for algebraic actions of amenable groups

Nhân Phú Chung and Andreas Thom

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Submission date: 27. Feb. 2013
Pages: 25
published in: Transactions of the American Mathematical Society, 367 (2015) 12, p. 8579-8595 
DOI number (of the published article): 10.1090/S0002-9947-2014-06348-4
Bibtex
MSC-Numbers: 28D20, 37B40, 20J06
Keywords and phrases: entropy, Torsion, Amenable groups, Algebraic actions
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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 reproved 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 infinity. These results extend previous work by Lind and Ward on p-adic entropy.