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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Entropy for automorphisms of free groups
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by Marie Choda PDF
Proc. Amer. Math. Soc. 134 (2006), 2905-2911 Request permission

Abstract:

Let $\sigma$ be the automorphism of the free group $F_\infty$ which is arising from a permutation of the free generators of $F_\infty .$ The $\sigma$ naturally induces the automorphism $\hat \sigma$ of the reduced $C^*$-algebra $C^*_r(F_\infty ),$ and also the automorphism $\bar {\hat \sigma }$ of the group factor $L(F_\infty ).$ We show that the Brown-Germain entropy $ha(\sigma )$ is zero. This implies that the Brown-Voiculescu topological entropy $ht(\hat \sigma ),$ the Connes-Narnhofer-Thirring dynamical entropy $h_\phi (\hat \sigma )$ and the Connes-Størmer entropy $H(\bar {\hat \sigma } )$ are all zero.
References
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Additional Information
  • Marie Choda
  • Affiliation: Department of Mathematics, Osaka Kyoiku University, Asahigaoka, Kashiwara 582-8582, Japan
  • Email: marie@cc.osaka-kyoiku.ac.jp
  • Received by editor(s): February 16, 2005
  • Received by editor(s) in revised form: April 20, 2005
  • Published electronically: April 11, 2006
  • Additional Notes: The author was supported in part by JSPS Grant #14540205.
  • Communicated by: David R. Larson
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 2905-2911
  • MSC (2000): Primary 46L55; Secondary 46L40, 46L89
  • DOI: https://doi.org/10.1090/S0002-9939-06-08318-3
  • MathSciNet review: 2231614