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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Fuglede–Kadison determinants and entropy for actions of discrete amenable groups
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by Christopher Deninger PDF
J. Amer. Math. Soc. 19 (2006), 737-758 Request permission

Abstract:

In 1990, Lind, Schmidt, and Ward gave a formula for the entropy of certain $\mathbb {Z}^n$-dynamical systems attached to Laurent polynomials $P$, in terms of the (logarithmic) Mahler measure of $P$. We extend the expansive case of their result to the noncommutative setting where $\mathbb {Z}^n$ gets replaced by suitable discrete amenable groups. Generalizing the Mahler measure, Fuglede–Kadison determinants from the theory of group von Neumann algebras appear in the entropy formula.
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Additional Information
  • Christopher Deninger
  • Affiliation: Mathematisches Institut, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany
  • MR Author ID: 56735
  • Email: c.deninger@math.uni-muenster.de
  • Received by editor(s): April 11, 2005
  • Published electronically: February 6, 2006
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 19 (2006), 737-758
  • MSC (2000): Primary 22D25, 37A35, 37B40, 46Lxx
  • DOI: https://doi.org/10.1090/S0894-0347-06-00519-4
  • MathSciNet review: 2220105